This happened at the gate, they did an upgrade at the kiosk to First Class.
How would any of the other passengers even have known they were in first class? I don't think they would have, so I seriously doubt it was a passenger complaint. I am starting to think the airlines story may make more sense, they saw somebody and asked about them, when told they were sitting in first class the pilot said not on my plane.
But with the little information released (and it's doubtful AA will release any video of a child with Downs acting up at the gate even if they had it) there's no where near enough information to draw any conclusions.