If you are looking for patches you see like on Emergency! that never happened here.
It most certainly did happen, in the Tucson area at least, and sounded very much like what you heard on Emergency!
I don't recall exactly when it ended, but through at least the late 1990s most transports in the Tucson area would call "MEDS Control" on Med 10 (which was operated by "Tucson City Communications" at Park & Ajo but accessed by all public and private ambulances in the entire metro area, and even out of area ambulances (like Cochise County or Santa Cruz County ambulances) transporting into the Tucson area. Ambulances called "MEDS Control" on Med 10 to request a "patch to [hospital name], and be assigned Med 1, 2, 4, 6, or 8 if I recall correctly (such vivid memories of this). MEDS Control would call the respective hospital and ask them to come up on that particular channel. ("MEDS Control, Paramedic 89, we need a patch with UMC... Paramedic 89 use Med 1 with UMC." [~3 minutes later on Med 10] "Meds Control, Paramedic 89, we are clear Med 1 with UMC, thank you.") Med 10 was repeated, but those Med channels 1 through 8 were half duplex - hospitals transmitted on 463.xxx and ambulances transmitted on 468.xxx. If the ambulance was relatively close and/or you had good elevation and a good antenna system, you could hear the ambulance's entire telemetry relay, often 1 to 3 minutes of dialogue between ambulance and triage nurse (initially) and sometimes ER doc for certain instructions. If a Med channel was already in use by one ambulance with a particular hospital when a second ambulance needed an urgent patch to the same hospital, MEDS Control (on Med 10) would ask the second ambulance if they wanted to stand by for the other ambulance to finish, or if they "needed hospital radio". If it was urgent, they'd say they "need hospital radio" and be assigned Med 9 with any hospital in the city. Med 9 was repeated, so in this case you could hear both sides of the entire telemetry communication on 462.950. Med 10 was also the primary dispatch channel for most ambulances in Pima County operating outside the Tucson City Limits, including even Rural Metro ambulances (MEDS Control would dispatch a Rural Metro ambulance on Med 10 to respond with a Rural Metro fire engine in Rural's own area, for example). MEDS Control also dispatched Rural Metro Paramedic 89 to CITY calls, because PM89 was based at UMC and staffed with 2 paramedics (the Tucson Fire staffing standard) and as a result was entitled to respond to City of Tucson EMS calls over a TFD Medic unit if PM89 was closer, as it often was in the UofA area.
The same sort of telemetry system could occasionally be heard throughout other parts of Arizona (beyond Tucson) between rural ambulances or helicopters, on the one hand, and hospitals throughout Arizona from time to time, except that in this case the patch was typically requested through EMSCOM (Phoenix) on Med 5. Because they were airborne, medical helicopters could easily be heard on 468.xxx giving patient reports to hospitals.
How is that for vivid details of certain scanner escapades of my youth!
Man, the days of VHF and UHF analog scanner listening in Arizona. What a time...