What would Bill Belichick do???
You think he would put up with criticism of him or his staff from an unproductive receiver ???
It is seriously not a question of whether Avant was right or wrong...Pro's keep dissension in house...they don't broadcast it for the world to see.
I agree with your point, but it's a bad example. The Patriots are a well run organisation. Under Belichick, Brady and co, they have built a dynasty. So every season they are a contender. You may hear the odd rumbling that Brady doesn't like them letting his receivers go, but ultimately they are a successful team that we've never been.
But what would Belichick or most head coaches do?
They would probably throw the guy in the dog house or cut him. If the players criticise the coach, then they generally end up being shown the door more times than not. The only time they might not get shown the door is if the coach actually wakes up and takes their point on board, and does something to sort out the problems his team faces, rather than living in cloud cuckoo land where they think their team is still a contender...