If she was severely mentally ill she may have been groomed into thinking she was handing him off to someone who would really care for him. We have seen mothers groomed by predators time and time again.
Also, I get the skepticism but LE seems to think this is an abused boy who showed up with bruises on his face wandering around alone. I don't think one abused child would research and pretend to be another missing child. Sure you can cherry pick one time a hoax has happened in the past but look at every time a missing child really was recovered after an abduction. They tell LE their name and date of birth. Shasta Groene, Elizabeth Smart, Jaycee, Jayme, Shawn, Ben, the list goes on.