So I was on a mission to rescue a transport ship, blew up a few Orions, then teleported to the ship. When my character loaded, I was actually my spaceship (surrounded, of course, by security officers) inside the ground mission.
I too had this experience. I stayed as a ship on the ground (when i teleported into the station after destroying the borg cube in the tutorial missions). This lasted about 3 minutes (i could move around and players could jump on me, so I Was interacting with the environment)... after this i got D/C again. Was able to open in-game ticket but didn't complete it before i got disconnected (hopefully it still went through).