Actually, what he protects is the perceived integrity of the NFL Shield, while its actual integrity can go hang.
See: Tape burning to protect the New England Patriots.
I know it was morally wrong to do what he did with the tapes, but honestly, if he didn't, the NFL would have had a HUGE shitstorm on their hands. Just think of all the bets that were made on that game. If the results were changed, what do you think would happen in Vegas? If there's one thing I know about gambling it's that you don't piss off Vegas. That's the real reason he burned the tapes. He wanted to keep his knees and his pet's head out of his bed.
As a Ram fan it pisses me off to no end but I know exactly why he did it.