Referees admitting they made a mistake but not being able to actually overturn said mistake

Seriously?  How stupid can the rules be?  During the Chargers - Broncos game yesterday (vested interest in the success of Philip Rivers), a game-changing play occurred which would have won the game for the Chargers.  Instead, the referee made the incorrect call, and because of some stupid NFL rules, the call could not be changed, even though he announced that he had in fact made the wrong call.  

Is it just me, or is there something wrong with that?  That makes no sense at all!  Dammit.