This is like Watergate.   It wasn't the crime, it was the coverup that got Nixon impeached.   Brady would have gotten off with a slap on the wrist if he had come clean with something like,

 

"I told the equipment guys I like my footballs a little on the soft side.  If I broke any rules doing that, I am sorry and I will accept whatever punishment the league wants to give me."  

 

Then the league would have slapped him on the wrist.   

 

But the fact that he lied and hindered the investigation, refusing to turn over his cell phone, and appears to have paid off the equipment guy to keep quiet, that is what the league cannot tolerate. 

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