Yes, the situation can be incredible as most clubs have a Head of Medicine, who maybe titled Performance Director or whatever, and this person doesn’t have a direct performance background but rather indirect via rehab, medical issues etc, and there are indeed major clashes.
I know of a club in England where the former Head S&C coach is suing the club due to unfair dismissal due to a new Head of Medicine arriving on the scene and causing anarchy. Several of the fitness staff have since left deeming the job unworkable. This is not to say this was the right or wrong move; the team are doing much better than previously…but like you said the in-fighting can be quite serious.