In current campaign Ko-Tun has the R5 Astromech companion. Can Ko-tun use Inch by Inch to move R5? R5 is friendly and would be getting the benefit of Ko-Tun's ability but would not be using the ability.

I think this is the correct interpretation. Just need confirmation if possible to convince the Imperial player for next mission.

Yes.

Also see the latest companion rules (from the FAQ). There is no longer the largely unnecessary restriction about "using" class, item, or supply cards.

Thank you. Didn't realize the FAQ took out some of that tricky wording.