But not the right place, and that's the problem. Apple support boards are seeing increasing message traffic about icons that vanish, or attach themselves to the wrong app. This seems a problem with iPhone 3.0. Older versions seem unaffected.
I saw this myself yesterday. My AT&T Navigator app which I am testing for a forthcoming review, somehow acquired my Reuters News icon.
I deleted the AT&T app and re-downloaded it, but that didn't help. I reset the phone and that didn't help either. Finally I did a sync with all the apps turned off in the iPhone apps tab, then did another sync with my apps on. That restored the proper icon, but some of my apps acted like they had been downloaded for the first time and I had to set them up again.
This is clearly a real bug that Apple will have to address. There are some other solutions floating around on the Apple message boards, such as deleting the app, downloading it again, and restarting the phone. If you have the problem, I'd suggest you try the easiest solutions first.
Some other users are seeing icons turn white, while other app icons simply disappear. One developer said this was a common issue before the final release of the 3.0 software, and he was surprised to see it now.
Let us know if you've got this affliction and what you did to fix it, and be sure to let Apple know.
Thanks to Steve for the tip.