Page 20 of the rule book says under the Moving Into And Through Objects section:
1) Execute the maneuver as normal, but skip the "Perform Action" Step
2) The Player rolls one attack die. The ship then suffers any damage or critical damage rolled.
I ran into this quite a bit at the KRT. The TO said that only applies when you overlap (and his definition of overlap is landing physically on the asteroid).
I meantioned that to people I was playing when they would run through an asteroid to roll damage and remind them that they couldn't take their actions. I have been playing it like that for a while now. The only difference I noticed in the rules were if you ended your move overlaping the obsticle that you also could not fire.
So I though I would check with you guys and make sure that I am not reading the rules wrong. If I am it makes that overlaping critical hit card not that bad.