The hull of the aircraft would probably be a bigger problem for reception than the altitude. People did commonly make calls from aeroplanes before they were banned.
But the radar thing showed that he never used a real radar in his life. He thought that the information on a radar screen was limited to the screen resolution and one pixel was the best you could get. He also thought radar display was 2D which is true on display level, but not at all on information level. You get speed vectors, estimated course and altitude information from even the modest hardware.