Perhaps -- though this was in the far South Pacific and I don't know that this airline offered that service. And, if they did offer it, how many people had paid for it?
It's not to be taken for granted that cellphone service was available. You'll have to remember that on 9/11, passengers on the doomed aircraft were picking up local wireless signals. They were in highly-populated areas and flying at abnormally low altitudes.
I can't say you're wrong, just trying to analyze the odds.
You are 100% correct. There is no cellular service available outside the plane.
There is an internal receiver (much like another cell phone) that receives your cellular call. A computer asks for a credit card number and after it’s verified via satellites, your cellular call is rerouted to the satellite phone. This is basically how the system works but it handles more that one call at a time.