While I have never served as an Aircrew memeber, I have learened a little about common pratices of air crews of that era. Door Gunners on helicopters were normally the enlisted crew member known as the "Crew Chief". A crew chief is a helicopter mechanic who is on flight status, meaning he has passed a physical exam certifing he is capable of serving on a flight crew, and as part of his job is assigned to a Helicopter during flight operations. Assualt helicopters such as a Huey or Blackhawk will have a crew chief who flies with the helicopter on every mission, an attatck helicopter such as a Cobra or Apache will have a crew chief who does not fly on missions because thier is no crew compartment, only two seat one for a pilot the other for a copilot. In comabt situations a "door Gunner" will be assigned to each assault helicopter in addition to the crew chief, giving the helicopter crew teh ability to man guns on both sides of the helicopter at the same time, this door gunner is almost always a helicopter mechanic, due to the fact that a person who is a designated door gunner would have to qualify as a "flight crew memeber" he would be subject to the same criteria for his rating as any other flight crew member, and there are only certain MOS's that are authorized to recieve flight pay, outside of special circumstances. The need to have a second machine gunner on a helicopter does not qualify as a special need, it is more of a routine cprocedure, thus wheeled vehicle mechanics, infantry men, and green berets are not often rated as official door gunners even if they were, they would probably get kind of mad being expected to fly and not recieve flight pay.
I am not in any way saying that there are not times when non air crew members fire from moving helicopters, to include the machine guns mounted in the doors. Generally pilots are a little funny about live fire coming from thier back seat, and prefer thier gunners to be at least familiar with the opertaion of a helicopter. I knew a man growing up who was a Chinhook pilot in Viet Nam he told me that it was not uncommon for them to mount 1919's on thier tailgate, this was not an approved modification, but was a fairly common site in Chinhooks in VN, according to other Viet Nam era pilots and crew chiefs I have asked about it, this proves that things that aren't exactly authorized happen.