Grrr ... I know this is pedantic, but can I make one common sense point? The exception proves the rule does NOT mean "because there is something which disobeys the rule, that means the rule must hold."

How could it?

"Prove" in this case is used in the same way as it is in the phrase, "the proof of the pudding is in the eating" or proofreading. It means test.

So ...

The exception proves the rule means "Take a case which you think is exceptional [the exception], test it [proof it], if the rule [the rule] still holds then it's probably a good rule."