Most statements don't hold in some contexts. Particularly, if you're advocating an implausible or subtly incorrect claim, it's easy to find a statement that holds most of the time but not for the claim in question, thus lending it connotational support of the reference class where the statement holds.

I think I agree with what you are saying. As a side note statements that include "Never. Never ever never for ever" need to do better than to 'hold in some contexts'. Because that is a lot of 'never'.