Your comment doesn't make sense in light of the fact that the family was forced to put the work on display, which doesn't sound like they "can do the other trappings of ownership but No One Else Can".
The article says: "Indeed, the only reason Mrs. Sonnabend was able to hold onto 'Canyon', Mr. Lerner said, was due to an informal nod from the United States Fish and Wildlife Service in 1981. {P} Even then, the government revisited the issue in 1998. Rauschenberg himself had to send a notarized statement attesting that the eagle had been killed...before the 1940 law went into effect. Mrs. Sonnabend was then able to retain ownership as long as the work continued to be exhibited at a public museum. The piece is on a long-term loan to the Metropolitan Museum of Art in New York, which Mr. Lerner said insures it, but the policy details are confidential."
This does not sound to me like it matches what you are saying at all. Quite to the contrary, it sounds like this work is quite special and important and for this reason was given these exemptions - this makes it quite likely for a sale to a museum to be approved, and the family has every reason to believe this.
So we must return to why you would say that a museum wouldn't or couldn't buy it (after saying earlier in your comment that museums were allowed to own such works, though the article does not make this blanket statement.)