I found another flaw. If you use Xenon's "Mods Can Edit Users" hack and then use my fix above, when a Mod edits his or her profile through the system, it erases the information in the fields that were hidden. I guess Xenon was correct about the fix and I think he posted his ideas in another thread so I'll go look and see what I can do.
If you don't use that hack, then no changes for you.