To get the permissions correct for installing Rollups on Exchange 2010 SP3, you will need to either disable UAC (not recommended) or you will need to launch the Rollup installer from an elevated command prompt (Right click and Run as Administrator) with the following command:
msiexec /update Exchange2010-KB2936871-x64-en.msp
This will allow the rollup to install properly. Other words, it will Roll Back and say that it Ended Prematurely.
Another note on Rollup 6 for SP3 is that it takes (at least in my environment) an extremely long time to generate native images for .NET assemblies. One of my servers took 45 minutes for this process. Wait it out and you'll be able to get it installed, just plan your windows accordingly.