"Usually someone with medical training decides "Yes, we need to land now" or "It doesn't require diversion, but go in hot". If there is no one with medical training, then the pilots can communicate with doctors (Mayo Clinic?) to decide."

That's basically how it goes. Any medical personnel who volunteer to help will either make the situation known to the pilot that they need to land or they can elect to conference with UPMC (University of Pittsburgh Medical Center - UPMC) to make a decision.