I've heard it called a "non-central example". That has a negative connotation though, I wish there was a more neutral term. The statement "all natural numbers are greater than 1" is false, and it's not helpful to object that 0 and 1 are noncentral examples.
(It's not a motte-and-bailey, that's about a particular sort of shifting goalposts)
(It's not a motte-and-bailey, that's about a particular sort of shifting goalposts)