No, Paul, most of these sites are hosted on MediaTemple, but I’ve even seen the behavior (where it forgets to exclude its own backup directory) on at least one of the test/development sites I’m hosting on my own local workstation (Mac OS X, Apache/2.2.22, PHP/5.3.15).
In all of these cases, manually adding an exclusion for the backup directory (new and/or old) has solved the problem.