that sounds really unusual; I've been running "lots" of Joomla! sites on DH for uears now, and have installed and upgraded using the "one-click" method, the "manual" approach using the shell, and the "patch" process all along and have never experienced that.
It almost sounds as though the "upgrade" process didn't comlpete. IF you upgraded using "one-click", the DH script that does the "upgrade" probably would have to change permissions (unless they ran it as "root", and I doubt they did that!) in order to over-write the files you "own", and then restore the correct permissions when done. IF the process got interrupted (by a "crash", etc.) it might not have reset the permissions. I'm interested in hearing what response you get from support on this one.
If this happened, Joomla should still "run", though I think there might be a likelyhood of "subtle" issues brought about by the "mixing" of the files from two versions.
If DH support can't get it sorted for you, you might just "running the upgrade" again, (or, even better, doing it manually from the shell, and see if that fixes the problem.