You don't necessarily have to be in country to receive an Air Medal. We have a couple of IPs in the HTs who've earned one for saving the lives of the aircrew after an engine failure in flight.
If you missed it, Dev covered that type of Air Medal a few posts ago vvvv
You can also be awarded Air Medals w/ no "V" nor a Strike/Flight number. There's quite a few helo guys that have them (w/ and w/out Combat "V's") for airmanship. Some examples are for SAR efforts or for saving the aircraft. One of the more recent engine failures in the HTs resulted in a full auto w/ lots of gas and two studs at night on a departure. The last word I got was that CNATRA or the Commodore had the paperwork in pretty fast because everyone walked away w/ only some spread skids.
You can also get a Distinguished Flying Cross (DFC) for an aerial feat not associated with combat. In fact, it is standard end of tour award for Thunderbirds.