'A' has got 1BTC legitimately. He sends out a transaction to transfer that one bitcoin to 'B' with a 1BTC transaction fee added on. (i.e. a bad request.)
'C' is a miner who cares nothing for integrity of the bitcoin system and only cares about winning blocks and selling the BTC he gets as soon as he can.
What incentive does C have to pass on the free 1BTC and not include A's transaction when putting the next block together?