Turns out that the Facebook Camera shortcut just said "Camera" - and of course it didn't open up the stock camera app (I think it showed up on the main screen and first in the apps list, too). Once he updated Facebook and the shortcut disappeared, the stock camera app was more obvious.
The shortcut itself was really confusing - it said Camera on it and it wasn't immediately obvious that it was Facebook-specific. You want to take a picture, you look down & see "Camera," and you click on it. Combine that with the fact that icons change underneath you a lot anyway (see also "Android Market becomes Google Play Store"), and you just default to reading the app name anyway; so you tap to open the first app whose caption matches what you're looking for.
I mean, why would anything but your stock camera app be named "Camera," anyway?