Just saw this movie and I think the story is being told by the little boy that was in the barn.
The first hint is in the mental ward where the black patient talks about his mind diverging to outer space, escaping his painful reality. I think this ward specialized in those patients. After kidnapping the psychiatrist James talks about crying wolf as a kid with that story, but something happened after, the movie didn't say what, as a kid to James.
I think he was really trapped underground, in a well perhaps, because there are a few references to tunnels in the movie. People probably didn't look for him right away because they remembered the barn incident and so he was in there awhile presumably. James hints of this when he was listening to the story on the car radio. He asks to change the station because he couldn't bear listening.
I think the psychiatrist was his psychiatrist as a child in real life after something happened to him and this is why she feels he looks familiar even in the first scene where they met. Just as the black mental patient, James has delusions of grandeur where he believes he has a strong mind and only he can save the world. I really liked this movie because it appears on the surface that it's about time travel, but it's actually about mental illness.