If a ship starts the Combat Phase on an asteroid, but then moves off of the asteroid during the combat phase before its Pilot Skill comes up (say, through Squad Leader or Ysanne+PTL+Boost), does it still get to fire?

It seems like it should, but the rules say if you are on an obstacle "during the Combat Phase" you cannot fire.

It should only matter when your ship activates. So yes you get to attack.

I'd have to agree with the above

I'll have to find the post that has the email but Alex D. responded that the only time being on the obstacle matters is when it is time to take the shot, even if that shot happens in a phase other than the Combat phase (Corran's double-tap).