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.
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?