Well maybe the OP was downgraded and Jon,L got a Battlefield.
Unfortunately Id say the OP is up a creek w/o a paddle. Im not gonna say her story isnt the truth. But whats to stop anyone from picking up any BP thats on the floor of the plane. So I fly in FC yet have a BP that says 16D on it w/o my name being the name on the BP, proves absolutely nothin. That is unless the FA that the OP dealt with will be contacted and in fact remembers what took place and is willing to send in a report that the OP did in fact sit in 22F and kept complaining they are a FC passenger.
But who was sitting in 1A, if a BP was printed for the OP had 22F on it was the person in 1A the person who belonged in 22F or someone else. If i was handed a BP that said 1A but wasnt in my name I doubt very much Id go and sit there.
Something doesnt add up