[jammaloo]

That's an interesting one, because it's misused more often than not, to mean what you are suggesting.

It's actually meant to say if someone provides an exception, e.g. "No parking on Wednesdays", then that proves the existence of another rule, e.g. "Parking is allowed". Since an exception, without a rule, makes no sense.

But, in my experience, people do use it to mean "Oh, this one thing is wrong, but that proves everything else is right", which does not track.

[FearNotDaniel]

No it's not. It's because the meaning of the English word "prove" has changed. It used to mean "test", which could of course have a positive or negative outcome. The modern sense of "successfully demonstrating truth" has caused this phrase to have the opposite of its original meaning.

[0] https://www.oed.com/dictionary/prove_v?tl=true

[xyzzy3000]

"The proof of the pudding is in the eating".

[BoppreH]

I think it's also appropriate to use it when the rule is so strong that exceptions are famous because they are exceptions. "Birds are capable of flight" is strong enough that penguins and ostriches are famous for being counterexamples.

[SketchySeaBeast]

But that's not following the saying - it's still not proving, it's modifying the rule. It shifts the rule from "birds can fly" to "most birds can fly". Pointing out that penguins can't fly doesn't make the case that birds can fly stronger in any way.