There was a pretty good video on this a couple of years ago: https://www.youtube.com/watch?v=QFv3QPNU6hw

TL;DW: The apparent tone shift is a result of interference from a bounce-path echo (from the ground) to the listener of the white noise emission of the aircraft, rather than expected doppler effect. This can be experimentally verified several ways, e.g., changing the bounce length (by moving closer or further from the ground) or by monitoring similar noises of known origin near an acoustically-reflective surface.