My local air ambulance uses Bell 407s an is operated by the Sheriff. They serve triple duty as not only an ambulance, but as law enforcement and fire suppression, as well.
They operate on two bands - primarily on a VHF repeater which is hard-patched to an 800 trunked talkgroup, and on the 800 system, itself.
The VHF operation is straightforward. They are the sole user and have immediate access to the dispatcher without the potential for queuing. On 800, it's a little more complicated because of simulcast overlaps causing phasing problems and reuse by counties that would be within line of sight at altitude. On-scene coordination can be done directly on the operational talkgroup, or through the hard-patched VHF system, either on the usual talkgroup or through console patching by the dispatcher. All ground operations are 800, with UHF and VHF in some specialty vehicles that have to interface with external agencies.
Where I lived before, there were two air ambulance services. One operated on their own VHF repeater system on business frequencies, as public safety VHF was very crowded there, the other used to use MED 9, but was moved for some reason to their own UHF business frequency repeater. On-scene coordination took place on a VHF fire mutual aid channel.
There was only one air ambulance in the region I grew up in. They were on a statewide 800 MHz analog trunked talkgroup and seemed to have good results. Now there are more, and those seem to be operating on the MED channels. Coordination used to take place either on pre-set agency response channels (I thought that worked very well) or common channels. The dispatcher had a database of who was on what channel and told the air crew which preset on the Wulfsberg the area they were en route to operated on.
As for the scope of the license, a license does not define height of mobiles. As long as the aircraft are enumerated in the mobile count, they remain primarily within the defined area of operation, and they comply with 90.423, they are "legal." Very basically, 90.423 requires aircraft to be below 5,280 feet, operate no greater than 10 Watts output power (practically, Effective Radiated Power is 10 W or less depending on antenna configuration), and their operations are "secondary" to land-based operations. Coordinators could put additional restrictions on ERP if there is interference to other operations.
An aircraft at altitude casts a tremendous footprint that could potentially "paint" a good portion of most states with potential interference.