Now the payloads that need to be recovered are just sealed to prevent saltwater contamination and fitted with flotation aids and dye markers so a recovery team can find them.
That's why they're going for a Corona style recovery.
The divers wait in two teams separated by a line, they notify the sub that then raises its periscope and steers between the two groups snagging the line. The divers then climb along the line to the sub.
[NB This was what they were doing ~1970 according to Paddy Ashdown]
http://en.wikipedia.org/wiki/Mid-air_retrieval#/media/File:C...
Thinking about it, it might be a weight constraint to cause them to use a helicopter. The sudden capture of an object weighing a few thousand pounds by a plane flying 350 mph could be too dangerous.
Batman even used it in The Dark Knight :)
http://en.wikipedia.org/wiki/Fulton_surface-to-air_recovery_...