Exactly. The Patriots had to push their case while someone could examine the knee in the condition that it was in - - not AFTER a surgery that could have gone either way. They received damaged goods. They should not have been expected to fix those damaged goods themselves before getting redress. What's the gripe?
The gripe would be the potential conflict between best interests of the team and best interests of the player.
If, hypothetically, it is in the best interests of a player to have a medical procedure to fix damage, and it is in the best interests of the team not to fix it - whether for a legal case review, as above, or simply to avoid a long rehab mid-season - then there is the potential for conflict. If you were the player, and medically the best thing for you was to undergo surgery as soon as possible, you'd want that surgery. That would be the gripe.
That said, I find it hard to see a conflict in this specific case. a) They probably have cameras at that Mass Gen place - best hospital in the world. Would be pretty easy to document the extent of the damage during surgery. b) The doctor is the expert in this situation, and could provide notes of the damage, whether or not the surgery is performed. It's not like they are going to open up the player's knee in front of an arbitrator and say "See!" Given that, there would be no benefit to the team of avoiding or delaying surgery. So no obvious conflict. Probably the opposite - much to their benefit to get inside the knee to see exactly the nature of the damage.
Again hypothetically, a grayer area is when a player has an injury that doesn't totally prevent him from playing, but puts him at risk of a worse injury. Say the team suggests continuing to play. Then it is up to the doctor, no different than decisions made by the trainer, to decide in the best interests of the player.
The benefit of having a guy like Dr. Gill as the official team physician is that he is the best. The team wants the most experienced, most expert physician serving the players on that team. The disadvantage is the direct relationship with the team rather than an individual patient. You have to trust that prominent physicians like this - and many surgeons are rumored to have bigger egos than team owners at times - will always decide based on the best interests of the patient.