In a game the other day, I ended up in the improbably situation where after completing my move, my ship was touching another one of my ships but not overlapping it. I play on a felt cloth and there is pretty much no accidental sliding of the ships. We were very careful about this particular measurement, and it came to the exact point of completing the maneuver and being in contact with another ship.

The question is, of course, so I lose my action? The rule state that you lose your action if you ship ends it's movement overlapping another ship, but this technically wasn't the case. I ended up conceding the action as ship to ship contact was made.

The same can be said for obstacles. If the movement template or ship brushes and asteroid without overlapping, does it count as hitting the obstacle?

From the FAQ:

Q: Can two ships be considered touching if neither ship overlapped the other ship during this round?
A: No.

If they don't overlap to the point of having to back up one ship or the other, they haven't overlapped. So no lost action, and they're not technically touching each other, which means they can still fire freely.