I think this is a better way of analysing this potion with tewari. If we start with the following position, and say black wants to stop white
a damaging the corner (tenuki is not the end of the world if there's something really important elsewhere, like a fight this was leaning for).
$$c
$$ ----------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . X X . O . .
$$ | . X a X O . . . . ,
$$ | . . . O . . . . . .
$$ | . . O . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,
- Click Here To Show Diagram Code
[go]$$c
$$ ----------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . X X . O . .
$$ | . X a X O . . . . ,
$$ | . . . O . . . . . .
$$ | . . O . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]
If black just connects at 1 then white has sente. What would white do? Tenuki? Maybe
a if local? White wouldn't play 2 to close off the left side with it so open, it's an endgame move, and a thin one at that. So exchange of 1 for 2 is significantly good for black (compare to what white can do if black tenukid before 1).
$$c
$$ ----------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . X X . O . .
$$ | . X 1 X O . . . . ,
$$ | . 2 . O . . a . . .
$$ | . . O . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,
- Click Here To Show Diagram Code
[go]$$c
$$ ----------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . X X . O . .
$$ | . X 1 X O . . . . ,
$$ | . 2 . O . . a . . .
$$ | . . O . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]
Then black plays 3 and white connects at 4. This exchange helps white, who got stronger on the outside, though black can capture the edge stone for endgame. Although white is a stronger shape, it's also rather heavy and needs an extension (but it's black's move). I think this exchange is less bad for black that the last one was bad for white, so overall black has gained a bit. As black has sente he can play such as
a/b to separate the top stone, pincer the left, or elsewhere.
$$c
$$ ----------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . X X . O . .
$$ | . X X X O b . . . ,
$$ | . O 3 O . . a . . .
$$ | . . O 4 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,
- Click Here To Show Diagram Code
[go]$$c
$$ ----------------------
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . X X . O . .
$$ | . X X X O b . . . ,
$$ | . O 3 O . . a . . .
$$ | . . O 4 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]
So, locally speaking, if black is sure white will play this way (big if) I think the wedge is generally better because black made one bad exchange, white made a worse one, and black got sente instead of gote.
What about that if? White has other choices: one would be to play atari of before and tenuki, or this atari and cover at 4. Can black hane at
a to cut and fight? That depends on a ladder as after
b he has to defend at
c.
$$c
$$ ----------------------
$$ | . . . . . . . . . .
$$ | . . . c . . . . . .
$$ | . . . 2 X X b O . .
$$ | . X 3 X O 4 a . . ,
$$ | . . 1 O . . . . . .
$$ | . . O . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,
- Click Here To Show Diagram Code
[go]$$c
$$ ----------------------
$$ | . . . . . . . . . .
$$ | . . . c . . . . . .
$$ | . . . 2 X X b O . .
$$ | . X 3 X O 4 a . . ,
$$ | . . 1 O . . . . . .
$$ | . . O . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]
Maybe black would do this. This might make sense for white if the top side is interesting and the left not.
$$c
$$ ----------------------
$$ | . . . . . . . . . .
$$ | . . . 7 . . . . . .
$$ | . . . O X X . O . .
$$ | . X X X O O 6 . . ,
$$ | . . X O . . . . . .
$$ | . . O 5 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,
- Click Here To Show Diagram Code
[go]$$c
$$ ----------------------
$$ | . . . . . . . . . .
$$ | . . . 7 . . . . . .
$$ | . . . O X X . O . .
$$ | . X X X O O 6 . . ,
$$ | . . X O . . . . . .
$$ | . . O 5 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]
Conclusion? Meh, go is hard.
It's easy to misuse tewari. Locally speaking, both the wedging in move and pole connection are plausible. Which is better here I don't know. It seems to me Calvin wanted to defend the corner weakness in sente so he could separate at f16 and set up attacks against h17 (but h16 instead of a pincer ruined that!), but how good are they? Maybe white could atari at d17 and cover at f16 if he doesn't like that, which would allow black to do better on the left side. But as you said after pole connection c12 still aims at b14 connection. I remember in my game against Haylee at the London Open (4th game move 35 
you are already off the rails.
I kind of want to play this hane.
I have scored a double sente. If not, he leaves the left side with an open skirt.