I think Mangina wants to win this game very badly, regardless of whether they have a playoff shot or not. No coach in football is sitting on a seat as hot as his, and an impressive win over Miami to end the regular season would not only leave a favorable last impression in the minds of the Jets front office folks as they decide whether to axe him or not, but also in the minds of any other NFL GM/Prez out there that might be looking to hire a new HC this offseason.
I could see two reasons why Mangini would want to throw the game.
1) He hates BB.
2)
If he was opposed to trading for Favre and cutting Penny, but was overruled by the FO, a loss to Chad would prove him right. (I had heard some rumors at the time of the trade he opposed it. But they were never confirmed)