Something similar happened to me when I was a kid. My whole family went to a church homecoming. When it came time to leave, my parents thought that I was in my grandmother's car. They didn't know until they got home. Not exactly the same situation, certainly, but close enough to illustrate that such a thing actually could happen, especially on an airplane, where groups don't always sit together, and may not even board at the same time.
It's been a long time since I saw that movie, so I don't recall the exact circumstances as to why and how the boy got left behind, but I think that at least that part of the story is possible. Him living alone all that time, when all that the parents would have had to do would have been to pick up a phone and call friends, relatives, or even the Police Department to check and see if he were at home, highly unlikely.