With some of the mystery behind how the final F seats are assigned, I recently was in a situation where I jumped ahead of the queue everyone is discussing here in the CPU thread.
I was originally booked on AA and during airport check-in was told I was in an oversold situation. AA offered compensation to fly a different routing (international => domestic). The international flight was a OW partner, and I assumed the domestic flight was on AA. However I later realized that they printed me a UA F boarding pass. So other airlines pay for last minute F tickets in situations like IRROPS and oversold situations.