Can we request one thing from the writer's of Lost....It's ok if you don't give answers, just no more questions!
Anyway, that lady was wearing some serious gear to have been on a helicopter. The suit she was using is pressurized with a positive pressure air mask....the kind of stuff you do if you're in special ops and jump out of an "airliner" at 35000 feet.
The helicopter may have been a second event unrelated to the parachutist.