These puzzles are entirely formal logic. Now you may not like or understand the intricacies of the logic/math and how it interacts with the English language, but the rules, and thus the solutions, are pretty objective and not open to interpretation.
Then the puzzle shouldn't use the word lie, because to lie can mean to be deceptive, and saying all your hats are green when you have no hats is clearly deceptive and thus can be considered a lie.
Then the puzzle shouldn't use the word lie, because to lie can mean to be deceptive, and saying all your hats are green when you have no hats is clearly deceptive and thus can be considered a lie.