IIRC, they added the hyphen because of the unfortunate pronunciation of the URL when it's not there.

It might have been a GOOD (or indifferent) idea a decade ago. But it's a bad idea if you're registering a new domain. There's different rules for old sites and new sites, and if you're making a new one, play it safe: don't have a hyphen.

Exception that proves the rule.

I don't think evidence against a belief works like that.

Proves: 3. To determine the quality of by testing; try out.[1]

The expression "The Exception that proves the rule" is just a wry way of saying "Well, that's not a perfect rule."

[1] http://www.thefreedictionary.com/prove

I think there's a little more to it than that. If the exception in question can be seen to have specific properties which are clearly the cause of its exceptionality, and if those properties can be seen to be rare, I think the exception supports the conclusion that the rule is a pretty good one, by showing what an unusual combination of circumstances is required for it to be violated.

That's pretty much what the saying is about. The existence of an exception proves the existence of a rule. The reliability of the rule can be estimated by considering the exceptionality of the exception.

I like the alternate interpretation that understands "prove" to mean "to test" in this situation, so that "the exception tests the rule".