I’ve seen this story twice now and still don’t get it. They had raised some money for treatment - why didn’t they just get on a plane and leave?
I'm guessing that the baby is hooked up to a bunch of monitors in the hospital, and they would have to unhook him and whisk him out, which is probably a crime of some sort. Plus, if he needs life-sustaining treatment to make the trip, they would have to have an American team on site to transfer the child from bedside to airport, etc. They couldn't do this without being seen or apprehended.