It is definitely a mixed bag in terms of effect. If Belichick wanted to (and I have no doubt he would if it undercuts his authority), then he could mandate that the team stay way from the facility. I still suspect much of the concern is more a product of salary cap concerns - specifically TB12 is illegal compensation for Brady that permits a lower salary cap hit for Brady offset by earnings channeled through TB12. It was alleged last year, so it is an ongoing concern.
2009 showed Belichick has no problem laying down the law. If it were a major issue effecting the team, then I expect he would mandate it out and let Brady do his thing. If the Pats players routinely fight the staff trainers and a program endorsed by Belichick, then I would expect Belichick would drop the hammer on Brady and tell him he can do whatever he likes with his trainer, but Patriots players are off limits. Belichick is not hated, but he is the law and knows how to win. Anything that impedes him will not be long in that organization. I have no doubt of that with him as head coach.
I don't otherwise see it as any different than the Type A personality who pushes vegan diets on you and touts the benefits. I doubt Patriots players would follow those regimens unless they believed it, and ignore it otherwise. It wouldn't seem to be the type of thing pitting TB12 players against the rest of the team or organization. These athletes can judge for themselves as they understand training, recovery and results and do what works for them.