Uninstall applet unpacks the JavaScrub-NoAdmin.exe file into C:\Users\<USER>\AppData\LocalLow\Oracle\Java\Uninstall and run it. Because exe file in *LocalLow* folder it doesn't have enough permissions. Here are some details:

http://www.windowspcguy.net/?p=173
http://msdn.microsoft.com/en-us/library/bb625960.aspx

"Not all application programs will run properly in a low-integrity process. A low integrity process does not have write access to most areas under the user’s local profile area of the file system or the registry under HKCU."

There are two solutions of the problem:
1. Unpack exe files into another folder (not into LocalLow)
2. Fix JavaScrub-NoAdmin.exe

Note that even if just put JavaScrub-NoAdmin.exe and UninstallJavaVersions.exe into LocalLow and run JavaScrub-NoAdmin.exe from console it fails with "Create-File-Wrapper:Access is denied".
If I just copy JavaScrub-NoAdmin.exe and UninstallJavaVersions.exe into
another folder and run with the same params - uninstallation completes
successfully.