I wonder if they make up something else?
They see people talking without signing all the time. So maybe they substitute some imagined thing for that. The mouths move, but the words just come to mind. When I hear people talking, I do not see written words in my mind. There is also the aspect of lip reading. No signing required. Do the deaf convert the lip movements to hand signs in their minds? Or just see and fell the things being said?
We visualize and feel what people are saying. Pictures and feelings. Not the physical movements of their mouths as an intermediate thing to consciously decode.
Words are things separate of the mechanical means to produce them. Immediately converted to so many things. So very easy to misunderstand, within and without.