It turns out that all the tips for Windows 7 and 8 rely on assumptions that are not valid in Windows Server 2012.

See here for some good Win 8 tips:

Removing Windows.old from Windows 8

For Windows Server 2012, I eventually figured out this kludge to get rid of the 16GB Windows.old folder:

1. Take a backup of the OS Drive on your Server (Usually C:).
2. As an Administrator on the local machine, or as a Domain Administrator, right-click on the Windows.old folder and choose Properties.
3. Choose the Security tab.
4. Choose the Advanced… button
5. Beside Owner at the top of the dialog, click Change.
6. Enter your own User Id.  Check Names.  Ok.
7. Now check the box that appeared for Replace owner on subcontainers and objects.
8. Click Apply.
9. When it’s done, Cancel out of the Advanced Security Settings and Windows.old Properties dialogs.
10. Then, reopen the Properties and select Security and select the Advanced… button.
11. Now hit the Change Permissions button.
12. Now click the Add button.
13. At the top, click Select a principal and put your own User Id in.  Check Names.  Ok.
14. Under Basic Permissions, click Full Control.  Click Ok.
15. Back on the Advanced Security Settings dialog, in the lower left check the Replace all child object permissions with inheritable permission entries from this object.
16. Click Apply.  Click Yes when it asks you to confirm.
17. Click Ok when it’s done.  Close the Properties dialog.
18. Now, close any other windows you happen to have opened in your frustrated attempts to get rid of Windows.old (I had many).
19. In Explorer, right-click the Windows.old folder.  Hold down Shift and select Delete.  (Shift will skip the Recycle Bin and just delete the folder and it’s contents).  Some time later, the Windows.old folder “should” be gone.  I did this on two servers and on one it disappeared, on the other two files were in use somehow.  Even after a reboot, those two files are still in use.  Weird.  They only take up 8K, so I’m going to ignore them.  One day, I might go after them again, but I doubt it.
20. It’s probably a good idea to force a reboot after deleting the Windows.old folder to make sure you didn’t just hose your server.  If you did, then you have a backup to restore from, right?