pretty sure that 'team docs' more or less come from affiliations teams set up with certain hospital networks.
i don't know if this is true anymore but i know for certain that ~7-8 years ago NYG team doctors came from Hackensack University Medical Center which is located minutes before the GWB in north jersey.
if i had to make a guess, based on our florham park team HQ, i would imagine the NYJ team docs come from Morristown Medical Center. after that, physician assignment may be somewhat arbitrary i imagine, and possibly depends on a combo of physician interest/availability and allocation of the 'best docs' at the institution as able.
i don't necessarily think that means that the best docs at the institution get assigned to the team, and if they still limit doc choice by institution, it doesn't mean that we'd have the best docs in the tri-state area.
of course, for serious and/or high-stake injuries, teams will always go out and search for expert opinion even if it means going elsewhere, and for good reason. it's why guys like james andrews kill it
Team docs are very dependent on the organization and the sport. Some teams charge for the right to be affiliated, some pick the Dr based on skill and some are picked through who they know, while others are how you said. It really does vary and sometimes even thougfh they're a "team" Dr, they're not the Dr used for surgery or many procedures that would take place during the year. It's really kind of wierd. I do personally know 1 team Doc, for an NHL team.
I know the Jets DR's in the past were not picked on skill, that much is evident by the Jets team "physician" being a concussion denier and the NFL's pointman on how head injuries were no big deal. A statement that was shown to be pure unadulterated horseshit. That jackass Pellman ran a completely fabricated study and somehow had an NFL job until 2016. Here's an article one of a 1000 on how this guy is a quack:
https://www.sbnation.com/2016/7/20/12239202/nfl-concussions-cte-elliot-pellmanLet this sink in to how the Jets are run by Woodrow, an heir to a pharmaceutical fortune, it's almost too funny to think about:
"Players who are concussed and return to the same game have fewer initial signs and symptoms than those removed from play. Return to play does not involve a significant risk of a second injury either in the same game or during the season."That was part of the Jets team Dr's philosophy on head injuries.......probably why Al Toon and Wayne Chrebet eat pureed peas.
