If this mission happens in a system with Imperial units, do the captured and capturing heroes move? My game group was split over the wording suggesting a necessary movement, or whether the "closest system" could be the one they were standing in.

I wouldn't say you have to move, since the closest system is the one you're in.

We had that last night and decided the system they were in was clearly the closest system

Correct. Closest can include the system they are already in.

I believe this was answered in an FAQ. If done in a system with imperial units then you don't move. zero is a smaller number than 1 and all.