To get the body out they would have to hover, send one or more persons down in the basket ... and pray the down draft doesn't knock anything loose onto the corpse removal crew. If it can't be done safely, they will not make the attempt.
Keep in mind that helicopters have altitude limits. Can they get above the corpse?
http://www.mod.uk/DefenceInternet/D...resNavyHelicopterCrewsForFutureOperations.htm might help. 10,000 feet is really high for a chopper, especially if you expect it to lift off.
I am a ski patroller, and we occasionally have to ship someone out by chopper. The White Mountain AZ helicopter evac uses an Italian "alpine-capable" make because it can lift off with a patient on board at the base of the ski area. That's just over 9,000 feet, and we're at their limit of safe operation.
They come in along the ravine and road leading in because they can't fly it over the ridges around the area. By the time they reach base they are doing 60mph towards us up the narrow canyon, barely 30 feet off the ground, the turbocharger is howling like a banshee to keep the bird in the air, and the blades are throwing a ground blast full of snow, ice, and gravel in all directions. It's impressive. It's dangerous to everyone on the ground.
Because they are landing they can stop the blades to load the patient, but our instructions if we get caught near the landing pad is "eat snow until the wind stops" because it can blow you off your feet. For a basket rescue, the blades can't stop, so your team would be working in a 40-60mph down-draft. Even in Phoenix, the choppers are used to drop the evac crews onto the mountains, they lower the victim and (if needed) the chopper meets them at the bottom because it's safer for the rescuers.
Anyone hurt further up the ski area mountain has to be brought down by toboggan to the pickup zone ... that led to an interesting incident last winter where an injured skier was calling 9-1-1 on his own and demanding med-evac get up to 11,000 feet to get him out. They bluntly told him they wouldn't risk losing a helicopter and a crew, and to shut up and take the toboggan.
We have wind limits to observe too ... the chopper can't maneuver as well at 9,000 feet as they do lower down, so if it's too windy they can't fly. In that case the patient goes by ambulance to the airport and a fixed-wing ambulance takes over.
Retrieval by a ground crew is more likely, but only if the body is in a place that the crew can safely enter. There are bodies on many mountains that will not be recovered because it's too dangerous. And if someone is fool enough to attempt to retrieve them, there will be more bodies in those spots.