Do you think that amongst regular people, there exists a liar who always lies?

It is a logic puzzle. It is not two regular (or academic) people communicating

Let's say that saying 'all my hats' implies that the set of hats is non empty, then you have the two following statements

    my-hats is not empty
    for every hat in my-hats, is-green(hat) is true

One of the points of this puzzle is to see beyond your social intuition. So yes, this puzzle plays on being able to figure out the logic while it goes against common social intuition.