So the rule does mean what I originally thought it did. In that case, I still disagree.
If you disagree about more than what you have just cited, you need to state it explicitly!
Although it does not actually have the word "disturber", the concept is there.
Correct. The fixed ko rule does not use that term.
The basic effect of the rule is that the attacking side (black in the linked example) always wins,
A formal proof for that still does not exist but AFAIK yes.
and that white is the disurber.
It is possible to invent the term disturber so that White would be it in the example. (Disturber might be defined about like this: "Given a ko, a position and the previous move not being a play in that ko. The player having the turn now making an - according to the general definition of "ko" - cyclical play in the ko is currently called its disturber. He will remain the disturber as long as the ko continues to exist consisting of the same set of intersections and until the subsequent move-sequence reaches a play (i.e. not a pass) that is not in the ko.")
Surely there is more than one alternative.
would be that the position is allowed to repeat once, allowing white to defend.
Such an alternative is possible in principle.
This rule would imply, stated or not, that black is the disturber.
It depends on how you define "disturber". Present a useful(!) definition to fulfil your claim! However, I guess you are intending something else here: Assessing ko winner and ko loser.
So a choice of one or the other is arbitrary,
I am not sure yet what you want to choose among. Different definitions of disturber? Different ko outcomes (who will be the ko winner)? Different ko rules? Depending on what you want, it might be arbitrary. However, disturber has been used, starting with Ing, along the meaning I describe above. What surely can be arbitrary (before we have specified the used ko rules) is the outcome of a ko.
and from a subjective perspective, I think a decision in favor of either is unfair in most cases.
In which sense "unfair"?
This is the question I am referring to. If you disagree with my assessment, can you tell me why?
Since it is still by far too imprecise what your assessment is, there is nothing I could already finally agree or disagree to. Again I ask you to clarify your statements! Then I would like to understand whether your statements are supposed to be praise or criticism of the fixed ko rule or whether they shall be neither. What do your statements have to do with the thread's subject?