I was wondering if the problem was processor related or if booting in 64 bit caused the problem. Of course, I could boot in 64 bit mode myself to test that on an old Mac Pro (MacPro3,1) but if I do get a kernel panic in 64 bit mode it doesn't mean that MacPro5,1 would not get a kernel panic in 32 bit mode. There are plenty of utilities to switch between 32-bit and 64-bit mode. Or you can hold down the 6 and 4 keys for 64 bit and the 3 and 2 keys for 32 bit.
Code:
$ cd /Library/Parallels/Parallels\ Service.app/Contents/Kexts/10.6/
$ file *.kext/Contents/MacOS/* | grep "[0-9] architecture"
prl_hid_hook.kext/Contents/MacOS/prl_hid_hook: Mach-O universal binary with 2 architectures
prl_hypervisor.kext/Contents/MacOS/prl_hypervisor: Mach-O universal binary with 2 architectures
prl_netbridge.kext/Contents/MacOS/prl_netbridge: Mach-O universal binary with 2 architectures
prl_usb_connect.kext/Contents/MacOS/prl_usb_connect: Mach-O universal binary with 2 architectures
prl_vnic.kext/Contents/MacOS/prl_vnic: Mach-O universal binary with 2 architectures
All the parallels kernel extensions are universal (32 and 64 bit) so presumably they have been tested in 64 bit. If Parallels tech support thinks it might be an issue with the processor then it's probably not related to booting in 64 bit mode but I just wanted to be sure.