Closest thing I can think of is Royval/Moreno. Shoulder popped out during a scramble and left Royval unable to defend himself during the fight. After the loss you can see Marc Montoya casually pop Royval's shoulder back into place and he seemed fine. IIRC he even insisted that he would've been fine if he could have made it out of the round and that he was even trying to pop it back in himself mid-fight or something. Apparently some kind of lingering preexisting injury that shows up often even in training? I dunno.
That said, I do agree with the sentiment of the doctor. Unless your cornerman is well-trained/experienced in reductions and the ringside physician is able to examine the limb afterward to ensure functionality then this is ultra sketchy and it's better to just take the L and not risk a career-altering injury.