For some reason, the GUI way of disabling offline files was greyed out, regardless of me logging in as local admin or a domainadmin. Maybe because it was set up with the computer in a previous domain? Don't know, don't care. A regedit fixes it all: edit HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\MRxSmb\Parameters\CSCEnabled and set it to 0x0. Reboot. Sorted.
Kudos to http://offlinefiles.blogspot.com.au/2010/10/disable-offline-files-registry-key.html for this info.