This person‘s argument hinges on trying to make two statements rather than one, I’ll illustrate with a quote:

> We know that the speaker always lies, so both statements must be false: my-hats must be empty, and it must be that it exists at least one hat in my-hat that is not green.

No. Since it is one statement as written, and the rules of common logic are not created by the liar, as I said up in the thread, either possibility is true. The person may have no hats or have one hat that is not green.