It's happened to me. Only major difference was I applied outside of the normal timeline since I was an experienced hier. Result was the same though, "we love you but can't bring you in this year; can you wait a year? Oh, and let us know if anything changes".
- First, you thank them profusely, and you say that of course, you'll spend another year of your life in limbo just for the chance to work for them in the future
- Second, you try hard to get an offer with the other 2. This is what they mean by "let us know if anything changes". So if ATK, Strategy& or Deloitte offers you a position, they won't care - but if Bain or BCG does, then McK will be more likely to jump and extend you a firm offer faster than expected
In my case, they called me back ~6 months later with a firm (written) offer, for a starting time 3 months after that (but over a year after I had first applied). So I ended up waiting ~9 months vs. the 12 they had indicated at first.
For now, I think you can treat this verbal offer as nearly certain. Try to use the coming year as best you can, getting some new life and/or professional experiences. Congratulations; I can't wait to officially welcome you to the MBB family :)
PS: Feel free to PM me if you want to discuss more, I remember how painful the wait was