So the rule is "Free parking on Sundays", and the exception that proves it is "Free parking on Sundays"? That's a post-hoc (circular) argument that does not convince me at all.
I read a different explanation of this phrase on HN recently: the "prove" in "exception proves the rule" has the same meaning as the "prove" (or "proof") in "50% proof alcohol".
AIUI, in this context "proof" means "tests". The exception that tests the rule simply shows where the limits of the rules actually are.
Well, that's how I understood it, anyway. Made sense to me at the time I read the explanation, but I'm open to being convinced otherwise with sufficiently persuasive logic :-)