Impersonation
Recently I read 'A Head Full of Ghosts' by Paul Tremblay. It's a novel, similar to the Exorcist, but different in that the entire sequence of events has been filmed by a TV crew for a show, and one of the protagonist is actively critiquing the theatric aspect of the show, while narrating the actual creepy events.
One of the characters asks the question "When we go to heaven, how do we know that our relatives we meet there are really our relatives, and not just some demon impersonating them?". Supposed the demon never acted out of character; then, there would be no way to tell an impersonation apart.
But then in real life, we do have instances of people acting 'out of character', or rather, abnormally. This can happen due to stress or illness. We wouldn't say or assume that the person in such a scenario is being impersonated in any way by anything. So why is it different in the case of the demonic possession?
Perhaps, it is normal to act abnormally once in a while. And when someone is 'normal' for an extended period of time, like the quiet little girl in horror movies, then one suspects that something might really be afoot.