When we researched medevac insurance we found in the fine print (where else) that the insurer's medical officer would make the decision which hospital they would evac you to for treatment. There also language that the facility would be the "nearest" one which could provide the services the medical officer deemed appropriate.
Short answer--READ THE FINE PRINT on any medevac policy.
We are currently using Air Ambulance--370/yr for a couple worldwide. They will evac you to the hospital of YOUR choice once you are admitted to a hospital. The admission is a critical component--you can not call and ask to be evac for a "strained muscle". We found this out when DW broke her knee cap but was not admitted but put in cast and cleared to travel home. Repair surgery would not happen for at least several days so swelling could subside.