Looking at Luther's response to your section about pushing, I see he confirmed that Kusarigama can move Omnitron. However, though I haven't seen the original version, the format of the comment suggests to me that the section originally read "Pushing is not the same as movement" and he suggested the language "pushing is a type of movement, but not all movement is pushing." which, combined with the fact that he only explicitly confirmed the statement about Kusarigama, implies to me that the FAQ may be wrong about Bunker's susceptibility to push in turret mode.
Now, I would normally tend to assume that since he assented to the section and didn't mention anything about Turret mode, that he was tacitly agreeing with you, though the ruling is counter-intuitive to me. However, the language "can't be moved" is used in scenario descriptions (specifically Omnitron acts 2 and 3) to describe things that seem intended to be stationary, such as buildings and scenario markers. The statement about turret-mode Bunker being susceptible to push implies that such things could also be pushed, which seems unlikely. Also, I wonder if suggesting the wording "push is a type of movement" was in fact Luther's roundabout way of telling you that "can't be moved" applies to push as well, particularly since he only explicitly confirmed your assertion about Kusarigama.
If you interpret his comment the way I do, and merely left the statement about Bunker in by mistake, it's an easy fix. If you feel that his comment confirmed the statement, I would request that we get an explicit ruling regarding whether targets which "can't be moved" can be pushed.
Edit: basic proofreading (spelling, punctuation)
Edit: just realized how badly I necroed this thread. Perhaps I should have started a new topic. If so, my apologies.