Let me address a couple of points.

First, about the idea that a play that loses 0.1 is not correct. I take that to mean that we are talking about opportunity loss, that the play gains 0.1 point less than the best play. That has a probabilistic interpretation. At the very end of the game we may interpret it to mean that 10% of the time it loses 1 point by comparison with the best play, and 90% of the time it does not, depending on the whole board. At the end of the game we evaluate plays locally. There may be any number of plays that are best, and any number of plays that are theoretically inferior, but with subsequent correct play, produce the best result. In a quiz, we still want to say that those plays are inferior, even if they happen to work out in a particular instance.
But in the fuseki we are talking about the whole board. A play that is normally inferior in a local area may be the best play, given the rest of the board. In a fuseki quiz we want that play to count as correct. We also want other plays that do as well to be considered correct. To say that a play loses 0.1 point is still probabilistic, but now the probability does not reflect our ignorance of the rest of the board, but our ignorance of the game tree. (Now maybe the best metric is not average point difference, but the difference in the probability to win the game, but let's stick with point difference. The argument is basically the same.) Suppose that we actually do have comparative point differences between two moves, and the average point difference is 0.1 in favor of move A vs. move B. Typically the usual difference will be 0. Most often, move A will score better than move B, but often move B will score better than move A, just not as often as the other way around. Because of our ignorance, we cannot conclude that move A is correct and move B is not. It is quite possible that both are actually correct with best play, but the players in our sample can handle move A better than they do move B, or maybe the apparent difference is due to randomness. It is also possible that move B is correct and move A is not. It is just unlikely, given our current state of ignorance.
We can make an educated guess, because of komi, that the first move in go gains around 14 points. Suppose that we have a play that we estimate gains 13.3 points, losing 0.7 points off of what we think is best play. That is only 5% less than what we think is right, and I submit that that is within our veil of ignorance. Now, point estimation is one thing that I research, and, IMO, that is a palpable difference. Normally, few strong players would consider making such a play. OTOH, with smaller differences, such as 0.5 points, it is likely that many of those supposedly weaker plays will score just as well or better than correct plays. And, in fact, many such plays are likely to show up in a pro game database. (The point, OC, is that the results with subsequent best play will often be the same.

)
Now, as a professional, I want to maximize my chances of winning, and will make the best play that I can, even if another play may be just as good. But that does not mean that I can say that a play that seems a little bit inferior to me is not as good or even better than my play. Thus, with some exceptions, I expect that any play chosen by a pro in a given fuseki position is likely to be as good as the best play (given perfect subsequent play), and some other plays, as well.
Second, about refutations. I think that refutations are found fairly often for joseki. We are talking about a relatively local area, we have well understood principles to judge results, and we can reliably compare results, even when we cannot readily compare results in terms of points. For instance:
$$Bc Joseki
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . . 4 . . . . . .
$$ | . . . . . 2 . . . .
$$ | . . . 1 . . . . . ,
$$ | . . . . . . . . . .
$$ | . . 3 . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,
- Click Here To Show Diagram Code
[go]$$Bc Joseki
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . . 4 . . . . . .
$$ | . . . . . 2 . . . .
$$ | . . . 1 . . . . . ,
$$ | . . . . . . . . . .
$$ | . . 3 . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]
This joseki had been around for some time before it was realized that Black could reasonably tenuki. Once that was pointed out, it was obvious, and the tenuki became frequent.
$$Bc Joseki?
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . 8 . . . . . . .
$$ | . 5 4 . O . . . . .
$$ | . . X 6 . 2 . 1 . ,
$$ | . . 7 . . . . . . .
$$ | . . . 3 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . 9 , . . . . . ,
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Joseki?
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . 8 . . . . . . .
$$ | . 5 4 . O . . . . .
$$ | . . X 6 . 2 . 1 . ,
$$ | . . 7 . . . . . . .
$$ | . . . 3 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . 9 , . . . . . ,
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]
This was played as joseki for a while, but then it was realized that the exchange,

-

, was not good for White, and White began simply to play at 8 right away.
$$Bc Joseki
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . 4 . . . . . . .
$$ | . . . . O . . . . .
$$ | . . X , . 2 . 1 . ,
$$ | . . . . . . . . . .
$$ | . . . 3 . . . . . .
$$ | . . . . . . . . . .
$$ | . . a . . . . . . .
$$ | . . . . . . . . . .
$$ | . . 5 , . . . . . ,
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Joseki
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . 4 . . . . . . .
$$ | . . . . O . . . . .
$$ | . . X , . 2 . 1 . ,
$$ | . . . . . . . . . .
$$ | . . . 3 . . . . . .
$$ | . . . . . . . . . .
$$ | . . a . . . . . . .
$$ | . . . . . . . . . .
$$ | . . 5 , . . . . . ,
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]
That led to this being played. Now, without the exchange in the previous diagram, this position was more vulnerable to an invasion at "a".
$$Bc Joseki
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . 4 . . . . . . .
$$ | . . . . O . . . . .
$$ | . . X , . 2 . 1 . ,
$$ | . . . . . . . . . .
$$ | . . . 3 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . 5 . . . . . . .
$$ | . . . , . . . . . ,
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Joseki
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . 4 . . . . . . .
$$ | . . . . O . . . . .
$$ | . . X , . 2 . 1 . ,
$$ | . . . . . . . . . .
$$ | . . . 3 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . 5 . . . . . . .
$$ | . . . , . . . . . ,
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]
So, while the extension to C-10 was still joseki, this variation began to appear.
Later,

became less popular, but I don't think that it has ever been refuted.
While I think that there are clear refutations in joseki, I am much more skeptical of refutations in fuseki. I have already mentioned how the Mini-Chinese went out of style for something like 150 years, and then staged a comeback. Fuseki books from the mid-20th century said that if you had a stone on a 3-4 point (komoku), you should make an enclosure rather than an extension to either side. (Thus, both the Chinese and Kobayashi Fuseki would have been considered incorrect.) The books not only offered those opinions, they showed refutations, variations intended to prove that those extension were incorrect, and thus how to answer them in a game. OC, the refutations were wrong. Here is another example.
$$Bc Refutation?
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . . a . . . . . .
$$ | . . . . 5 2 . . 4 .
$$ | . . . 1 . 6 . . . ,
$$ | . . . . . . . . . .
$$ | . . . 3 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,
- Click Here To Show Diagram Code
[go]$$Bc Refutation?
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . . a . . . . . .
$$ | . . . . 5 2 . . 4 .
$$ | . . . 1 . 6 . . . ,
$$ | . . . . . . . . . .
$$ | . . . 3 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]
Another thing that the books at the time said was for White not to extend to 4. The kick at 5 was offered as a refutation, because

is too close to

and

. By tewari, if those stones had been played first, White would have extended one more point. This was relatively new thinking, because, even though tewari went back centuries, in the 19th century players had often extended to 4 without much concern.
But

has made a comeback, as well. One reason, I think, has to do with the tenuki after the slide to "a".
$$Bc Joseki
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . . 4 . . . . . .
$$ | . . 5 . . 2 . . 6 .
$$ | . . . 1 . . . . . ,
$$ | . . . . . . . . . .
$$ | . . . 3 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,
- Click Here To Show Diagram Code
[go]$$Bc Joseki
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . . 4 . . . . . .
$$ | . . 5 . . 2 . . 6 .
$$ | . . . 1 . . . . . ,
$$ | . . . . . . . . . .
$$ | . . . 3 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]
Often White had been able to count on Black to answer

with

, and then White could extend to 6 without any problem. But if Black played tenuki, White could not count on getting the extension on the top side. So if White wanted to guarantee getting that extension, he started making it right away. It turns out that the willingness of players in the 19th century to accept a little bit of overconcentration may not have been so bad, after all.
The battle of ideas in the fuseki is dialectical, and, even though progress is made, supposedly inferior plays cannot always be counted out, so great is our veil of ignorance.

Edit: Corrected the pincer diagrams. I had misremembered.