The exact title of the capacity is 'theory of mind' - for example, chimpanzees have a limited capacity for it in that they can understand others' intentions, but they seemingly do not understand false beliefs (this is what GP mentioned).
Theory of mind is a distinct concept that isn't necessary to explain this behavior. Of course, it may follow naturally, but it strikes me as ham-fisted projection of our own cognition onto others. Ironically, a rather greedy theory of mind!
If apes started communicating mongs themselves with sign-language they learned from humans that would measn they would get more practice using it and they could evolve it over aeons. Hey, isn't that what actually happened?
This seems like a rather awkward way of putting it. They may just lack conceptualization or abstraction, making the above statement meaningless.