Bear in mind that the studios, although rivals, aren't completely against the idea of doing cameos that cross studio lines. Apparently the Oscorp Tower almost made it into The Avengers (it was cut because by the time the building's design was finalized, the Avengers NYC skyline had already been rendered, and there wouldn't be time to include it). And because of a bit of contractual legerdemain, there will be a helping of shawarma relating to X-Men: Days of Future Past after the credits of the Amazing Spider Man II (but that isn't indicative of any coming cross-over between Spidey and the X-Men).
There is certainly precedent in Hollywood. Look at 1988's Who Framed Roger Rabbit?
I see no reason the same sort of thing couldn't be done for the Marvel Universe properties. Fox has already said they'd be up for it.
The point is that these sorts of crossovers don't have to be huge, multi-movie-spanning deals. Just a couple of minutes here and there, woven in and between the various studios, could not only cement the franchises as belonging to the same larger universe, but would also serve to raise all boats as people who like Spider Man might be a little more inclined to see Fantastic Four, and Avengers will pull in some more X-Men fans.
It worked for Roger Rabbit. It can work for Steve Rogers.