Here's a possible solution (or at least a further clue) for late-comers who have tried everything suggested here and are still having this problem...
I tried deleting apps, re-authorizing, re-indexing, etc. Nothing solved my problem. Until I noted a certain comment on this forum about Spotlight indexing a remote hard drive. Well, I happen to have a separate MacMini and a MacAir residing on my ethernet, and they both belong to a different user/Apple ID.
Spotlight appeared to be indexing these remote drives, and in the process, may have been getting the AppStore confused about who owns what. In any case, I added these computers to my Privacy list in Spotlight preferences, and my problem was solved. No more "You have updates available for other accounts..." It's downloading just fine.
To try this fix:
1. Open System Preferences.
2. Select Spotlight.
3. Select the Privacy tab.
4. Click '+' to add a folder or drive to block.
5. Browse to a network device. Be sure you navigate to the shared hard drive itself and not just a folder on that drive. Add it to the privacy list.
6. Close System Preferences.
Now see if your downloads will work in the Mac AppStore. Mine did.
Good luck.