This is what the all-knowing AIM says about 'Lifeguard':
b. Air Ambulance Flights.
Because of the priority afforded air ambulance flights in the ATC system, extreme discretion is necessary when using the term "LIFEGUARD." It is only intended for those missions of an urgent medical nature and to be utilized only for that portion of the flight requiring expeditious handling. When requested by the pilot, necessary notification to expedite ground handling of patients, etc., is provided by ATC; however, when possible, this information should be passed in advance through non-ATC communications systems.
1. Civilian air ambulance flights responding to medical emergencies (first call to an accident scene, carrying patients, organ donors, organs, or other urgently needed lifesaving medical material) will be expedited by ATC when necessary. When expeditious handling is necessary, add the word "LIFEGUARD" in the remarks section of the flight plan. In radio communications, use the call sign "LIFEGUARD" followed by the aircraft registration letters/numbers.
It only talks about and 'urgent medical nature' and 'carrying patients'. It doesnt say anything about a requirement for the patient being in a life-threatening situation. A good number of inter-hospital transfer flights that routinely use lifeguard would not qualify under that definition.
I don't know what the patient in this case was treated for and what the degree of urgency to get to Mayo was. The patients personal physician came along, unless he was heading for the nightlife of Rochester, he presumably came along to monitor and attend to the patient during the transport. If the PIC found it appropriate to use the lifeguard call-sign for this situation, I don't think we have much cause to second guess it.
Flights done under the air care alliance umbrella are for the most part a convenience to the patients involved and care is taken that there is NO medical urgency in the missions involved. To reflect that different nature of medical compassion flights, the ACA board got the FAA to issue the CMF callsign.