I've never had a misunderstanding involving any of the OP's examples, except the one about exceptions. (And what does that prove?) I've actually had several arguments that went like this:

Interlocutor: [generalization] Me: But what about [exception]? Interlocutor: That's the exception that proves the rule.

My citing of an exception seemed in no way to weaken my interlocutor's confidence. Was this because the "exception" cliché was just a cached phrase that stepped in to block a change of mind?