I agree it's very possible that you can't get it successfully installed under existing siding, without removing at least the bottom siding. But since the problem here is ice damming, to apply ice shield to the roof deck and not have it extend 4 - 6" up the walls is a recipe for doing the whole job over. If water backs up, it's going to get in at the wall.
I think a big part of the problem here is the same as in the thread with the poster that had laminate floor installed and they didn't take care of where it meets the wall because the concrete was irregular. She was proposing to get the same contractor back to try to deal with it. Big mistake. What she needs is a finish carpenter. And here what the condo board should do is get some carpenters to quote on dealing with removing/replacing the siding. The roofers get set in their ways, and want to half-ass their way out of dealing with siding. If I were the roofing contractor, I'd either learn how to do the siding, or else have a carpenter buddy to sub out that part of the job.
Another common problem here is that typical condo board is folks with little or no experience in anything, so they get hosed all the time.