> The word "prove" used to also encompass the meaning of "challenge" or "put to the test".

Yes but "There is little evidence of the phrase being used in this second way.", citations located at wikipedia.

So I think it makes more sense to go with the interpretation of "if someone lists an exception, then that's proof of a more general rule that it's an exception from". But with that use, something specifically has to be an exception. Anyone applying "exception proves the rule" to an anecdote is using it wrong.