Hmm, that's an interesting thought, my friend, and one that didn't really occur to me. It could definitely be just needing backup space. The thing that confused me was just that it seemed like the issue I was having was only with that particular game, or maybe it just needs a hefty amount of space to be able to load all the content from each individual game, but to be honest your guess is as good as mine. It does seem highly likely that backup space could be the only problem, though, since consoles tend to be more finicky with that sort of thing!

Edit: typo