That's also not what "an exception proving the rule" is either. The term comes from a now mostly obsolete* meaning of prove meaning "to test or trial" something

That's also not what "an exception proving the rule" is either. The term comes from a now mostly obsolete* meaning of prove meaning "to test or trial" something. So the idiom properly means "the exception puts the rule to the test." If there is an exception, it means the rule was broken. The idiom has taken on the opposite meaning due to its frequent misuse, which may have started out tongue in cheek but now is used unironically. It's much like using literally to describe something which is figurative. * This is also where we get terms like bulletproof - in the early days of firearms people wanted armor that would stop bullets from the relatively weak weapons, so armor smiths would shoot their work to prove them against bullets, and those that passed the test were bullet proof. Likewise alcohol proof rating comes from a test used to prove alcohol in the 1500s.