Classic ITE question, a well taped tube can advance with neck flexion and pull back with neck extension. If neck was well extended when taped and is now flexed significantly in prone, it could definitely advance the tube enough to cause a problem. I also agree that it's reasonable to flip to fix if it can't easily be adjusted.
Or you could be an idiot like myself and prone a patient WITHOUT taping in the tube (whoops!). C-spine injury so he was in pins, thankfully making it easy to tape. Before everyone loses their minds, I agree that this was totally idiotic and never should have happened.
Now that that is behind us, I'll describe a few events that led to it. Took forever to get fem art line (can't remember why upper extremities weren't an option), guy had crappy heart (EF15-20%), AICD, vertebral artery dissection and numerous c-spine fractures after a fall. Had all the other health problems you expect (CKD, DM, AFib, etc.). Immediately after an asleep fiberoptic intubation, my attending starts telling me to do stuff (that does not involve taping in the airway) so I do those things, assuming that my attending is taping the tube -- this is a very common practice here, attendings usually say things like "go put in your IV and I'll tape the tube."
Anyway, the neurosurgeon puts the head in pins and takes the head for the flip so I never returned to the head personally after putting the tube in.