Parallels' problem isn't case-sensitivity.
With the help of Drew Thaler's instructions on how to grab disk access by running an app in gdb, it looks like the bug in Parallels Workstation was even weirder than the case-sensitivity problem. Parallels uses QT, a cross-platform GUI toolkit to handle user interface presentation, rather than the much-more-common-on-OSX-but-not-cross-platform toolkit called cocoa. Unfortunately, it follows my library search path to get to QT. My installation of QT is broken. (I've known this for a while and haven't had the time to rebuild it from source). Why doesn't Parallels force inclusion of QT from the app bundle? I don't know. Bug report filed.
See the extended entry for Drew's instructions (thanks Drew!)
[start target app under GDB, and break early in the initialization process]
% gdb /Applications/Parallels/Parallels.app/Contents/MacOS/Parallels
(gdb) b __dyld__ZN4dyld24initializeMainExecutableEv
(gdb) run
Breakpoint 1, 0x8fe03116 in __dyld__ZN4dyld24initializeMainExecutableEv ()
[now that it's launched and we can target it, in another window, run fs_usage]
% sudo fs_usage -wwf filesys Parallels > ~/Desktop/fs_usage.Parallels.txt
[back in the gdb window]
(gdb) continue
[app does whatever it does, and crashes. We're done.]
[ctrl-c to kill fs_usage]
[back to gdb]
(gdb) kill
(gdb) quit