This topic came up last night with my team. I had asked the students "do you have to move to assist" as a bait question, and I said that you do not technically have to.
The robot I had in mind would be able to sit by the human load station, receive a ball in the top from a human player, and LAUNCH it out in some directed way.
I wouldn't argue that this is a very practical design, but I can't see that it would be ruled illegal or "not a possession" to a referee. This might not meet your definition of "immobile" if you are referring to nothing on the robot moving (actuating) vs. simply staying in a fixed position.
However, to the other thread's point. If an alliance robot was capable of both setting the ball on an alliance partner as well as pick it up off of them, I would call this a grey area. Yes, if you do that to an opponents ball you are "possessing it", but I think the very definition of an assist (in English) implies some action being taken by the one assisting.
Just speculation though, your guess is as good as mine.
edit:
Ironically, as I went to add the definition, I found this second (rarely used) definition of assist in Websters.
1: to give support or aid <assisted at the stove> <another surgeon assisted on the operation>
2: to be present as a spectator <the ideal figures assisting at Italian holy scenes — Mary McCarthy>