The VLC example mentioned below in fact supports this: Apple was absolutely fine with it being in the store until Rémi Denis-Courmont filed a copyright violation with Apple asking them to take down the version that had been posted there. Apple didn't take initiative to remove it themselves.
What if someone sold an iOS app that could be downloaded from the iTunes App Store that "contained" the source code? (Actually, it would detect whichever app started it and would download the source on demand.) Combine this with a free app and service that lets people use on-air provisioning to get modified versions of apps?
I think "this software is for personal use only" is the main (only?) GPL incompatible parts of the App Store terms. I don't know if it's a possible outcome, but I wonder if there's some way to force iOS to be an OS where you can run any programme (i.e. no App Store needed), if there is GPL software. This is clearly not something Apple want, so they may be trying to nip that problem in the bud by setting things up to stop GPL. I believe some sort of Microsoft app store explicitly bans GPL.
Apple do officially care, and they only officially allow things in that match their rules. If you told Apple that the software was GPL, they would probably care and pull it.
The reason VLC was there for long was because Apple clearly don't check things in the App Store very much (examples like this, and various scammy apps, and pirated software back this up). However once (one of) the copyright holders noticed it, they informed Apple that Apple was distributing copyright infringing software, and Apple promptly acted.
GPL software on the iOS App Store is about as legal as copying DVDs of Hollywood films and selling them yourself, or copying someone else's closed source software and uploading it to the App Store.
Remember, GPL software is often based on other GPL software that someone else wrote, and released to you under certain terms (the GPL). To distribute it via the App Store goes against the spirit and letter of those terms. It should be clear why some developers are annoyed about people who do that.
That's a common misconception, but actually has nothing to do with the GPL/App Store incompatibility. You can distribute a modified version of the app in source form, and let the users compile it and install it on their own device. You just can't distribute a modified version through the App Store, but that's OK. GPL has no requirement that people who modify GPL code be able to distribute their modified programs through the same channel they obtained the unmodified program.
The GPL/App Store compatibility arises from the App Store terms of service. In order to download from the App Store, you have to agree to things, such as not reverse engineering what you download. GPL prohibits distributing GPL software with additional restrictions, and the App Store terms count as additional restrictions.
Y'know I'm not sure this is something the GPL would care about. I mean if Apple sell GPL software (gcc), but if I modify gcc Apple are unlikely to sell my fork on apple.com, that doesn't mean Apple are breaking the GPL.