instead of going through and making more and more edits, I finally figured out what the problem is here - there are at least two logics being used here - one set theory, in which case for vacuous truth I guess it's true that all the hats are green if you have an empty set, and the other linguistic logic.

In many forms of linguistic logic you need to have an existent hat to have the property green, therefore if you do not have any hats you have no green hats. Which is my preferred method of dealing with this.

And obviously there are other forms of logic, as https://iep.utm.edu/liar-paradox/#SH3c

Is the column that was linked more likely to be interested in linguistic logic games or formal mathematical logic games? I'm guessing the second, in which case I guess it's true we can conclude A - but I inherently dislike vacuous truths when applied to logic, especially language like this where the normal argument that the second parameter "Green" is never evaluated because we do not have the first "A hat" in the empty set seems suspect to me because we know what Green is separate from a hat, we just need to know if there is a hat we can assign Green to.