That's an old OFP "feature" : I believe the classic workaround is something like you've described : that the group is moved into the vehicle they need to be moved into a fraction of a second into mission start, for instance in a trigger or a waypoint. Start with a short black-in and no-one will be any the wiser
As to hiding the player's location - I assume you're playing Cadet mode then, since in Veteran (in the default difficulty settings) you can never see the player's or any body else's start location on the map. If it's that important, I suggest you simply place the player in some dummy location (out in the sea, or on some abandoned island), and then at mission init you move them to their intended location.
Hope that helps,
Wolfrug out.