NEW YORK—The Yankees were still out on the field, in the final moments of losing a game early Sunday in front of a funereal crowd, when a small group gathered in the athletic trainer's office deep inside Yankee Stadium.

Dr. Christopher Ahmad, the Yankees team physician, was flanked by general manager Brian Cashman, the team's trainer, Steve Donahue, and the revered former Yankee manager, Joe Torre.

And...