If you get into the medical details of the case, it becomes more and more clear that Mazzagatti's call was the wrong one.
In a show with the level of scrutiny that the UFC receives you are correct, it would be very irregular to stop a fight due to a cut without consulting a physician. In smaller shows it happens fairly frequently, particularly for amateur fights. If a cut is inside the orbital socket, against the lines of the face you KNOW that fight needs to be stopped. You DON'T need a doctor to make that call.
The reason you call the ringside doctor (and smaller promotions don't do it because the fans don't have the same level of patience, but they should, because it's the smart way to handle the call) is to check out the cut, see if it's debilitating.
In the case of Hamill, the cut may or may not have been debilitating. It had nothing to do with Hamill's decision (and it was Hamill's decision) to concede the bout.
The problem is that Mazzagatti either did not know or did not exercise proper protocol in calling for an end to the fight. The only reason he needed to use the instant replay (which I'm for, but was excessive in this instance) was to reevaluate and retroactively upgrade his point-deduction to a disqualification, a decision that was not warranted based on the evidence I've already presented.
But, again, you've totally missed the mount.
Of course Mazzagatti has a right to stop the fight.
He does not have a right to issue that disqualification, because there was no connection between the illegal strike and Hamill's decision to give up.
His point is that what you are talking about is completely irrelevant to this scenario. He stopped the fight because Hammill sId he could not continue. Hammill said that because of his shoulder. None of that had anything to do with illegal elbows or cuts around the eye.
Up to speed?