> In the world of logic puzzles, it is understood that a "liar" never makes a true statement, and that "vacuously true" statements are false.

I agree with the first stipulation, but, outside of Lewis Carroll's puzzles, I think that the second isn't true. For example, I believe you'll find just the opposite in Raymond Smullyan's books.

Which seems to be an untenable premise.

"I never make a true statement" says the liar.