Rule 3-1-2: On matters of judgment, the referee shall have full control of the match and the decisions shall be final, based upon the NFHS wrestling rules and interpretations.
Rule 4-2-3: References to the designated medical person worded this way: "...a designated, on-site meet, APPROPRIATE health care professional..."
This means you could have some medical person who is not necessarily expert/qualified to diagnose communicable skin conditions - and, you may conclude that person is not APPROPRIATE for this situation.
Case Situation 4.2.3B: In this case, a note from an appropriate health care professional says the wrestler can compete as long as the condition is covered. From the ruling for that case: "If the wrestler has a skin disease that is in the communicable stage, the wrestler shall not compete REGARDLESS of any statement from an APPROPRIATE health care professional.
So, it would be need to be an exceptional circumstance, but there is support for the notion that the referee could overrule the appropriate health care professional - even if it is the designated, on-site person. But, I will emphasize this very strongly, it would be very complex to thread the needle if a referee ever felt they should overrule a designated, on-site, medical professional's opinion. I would never suggest that the decision by that medical person to disqualify a wrestler should ever be overruled. However, if there ever was a circumstance to over rule them, it would need to be a case where the professional clears the wrestler, and the referee is saying "No". I have never heard of such a situation where a referee has over ruled the medical person onsite.