I don't know when I'll be able to get my BO2 disc back into my console, but I had a similar problem a while back. The reason I asked about how many slots you had left is because, if I recall correctly, it was showing I should have had enough slots open, as well, and it turned out I did not. I could be mistaken, but that's what I remembered when I first saw your post. I'm not an employee of ATVI so this is not my day job. Please forgive me if it takes a while to respond.
My issue was slightly different. I discovered it because I was trying to save some game clips from Theater. Your Vault spaces are for anything you want to save, whether a still pic, game clips, or custom games. What I did was to upload clips to YouTube then deleted them from my Vault. Doing so freed up space and I had no issue.
Like I said, this may not be the exact same issue, but that is what I recall off-hand. I know that, at most, I was only trying to save one or two custom games (if any. I usually don't make any, but I think my lil bro was trying to tell me how it worked so I was tinkering with it).
In any case, I will bookmark this thread and when I can, I will check into it further to see what I come up with.