Enable offline file sync for computer owner only

Solution 1:

You're running into a design-limitation of Offline Files. It is a per-machine cache, enabled and disabled at a per-machine level. Offline Files limits visibility of items to users who are authorized to view them, but there is a single cache on the machine. You can't disable the caching functionality for just certain users on a machine.

There just isn't a granular level of control to do what you're looking for. The community asked for it in Windows Vista, again in Windows 7, and still didn't get it in Windows 8. (There's some kinda, sorta functionality in Windows 8 with the "Primary Computer" functionality of Folder Redirection, but that's not a change in Offline Files-- it's just a change in Folder Redirection that impacts the Group Policy setting to always make redirected folders available offline as a side-effect.)