I don't think there's any dispute that the city owns the land now. If they didn't, how could they claim rent? From what I can figure out from the bits and pieces is that the land was owned by the city, part of the same parcel that the large adjacent park and the nearby museums were built on. The Scouts offered to build a building on one lot, then give it to the city in return for the $1/year rent, which was "perpetual," but included a clause that allowed the city to end it with one year's notice.
What I've noticed in all of this is that the Scouts don't seem to be claiming any particular legal leg to stand on. They're making a moral argument instead. It seems that if they did have some legal grounds to fight this, they'd be all over it.
I agree that if that's true they should be all over it, but there are a lot of examples of where they clearly are on the moral and legal side, and yet they do nothing.
I can't come up with a specific case right now, but I do remember O'Reilly taking the Scouts to task for just letting someone run all over them when they had the legal high ground without as much as a whimper.