I've never spoken directly with MedLink when I've been called for in-flight emergency, but have communicated through the captain where indicated. What I've noted is that the captain remains in charge of the situation as they know all the factors that I don't - what planes can land where, what the on-ground regional medical facilities offer and how long it takes to get there, how much O2 is on the plane for sick passenger use, etc. I presume they speak with MedLink about these factors and may take my assessment into consideration as well. I haven't had any disagreements with MedLink (as reported to me through the crew) about what treatment is appropriate for the patient. If the patient is sick I always hope the plan lands very soon, but it's not really up to me, I just deal with the situation as best I can as it plays out.
It's always seemed a team effort to me when dealing with a sick passenger mid-air. If there is more than one practitioner volunteering, then working out who can/should do what, and collaboration with crew as to equipment, space to treat the patient - all those are taken into account. Maybe I've been lucky (or unlucky, depending on viewpoint) but when called to assist, it's seemed to me that everyone has behaved professionally and done their best to help the sick person.
I always keep my own "contemporaneous notes" about what happened during the incident, but no legal problems have arisen.