Why wouldn't the condo people want to do it? Because it's their money.
I would think you could remove that portion of the roof (shingles) to see the plywood underneath. Once to this point, I would assume the professional roofer they have on staff could fix where the vent used to be. IE- seal it with another piece of plywood cut to fit. Then re-shingle this area.
I am no roofing expert though. That idea just makes sense to me.
You're more than welcomed to contact a few contractors on this site. It's encouraged! Get a couple quotes on how to fix this permanently and take them to your office. By "own the outside", do they mean the building's outsides or the lawn and maintenance? Big difference.
If they really own the outside of the building, it is their problem to deal with. I would assume your mattress is too. And any painting or repairs that need to be made inside.
I hope you have all the paperwork from when they fixed it the first time. I suspect they are not going to willingly write you a check for all the damage. You can expect to see them in court.