> They feel that the GPL is incompatible with Apple's distribution mechanisms, since it's impossible to "distribute" a modified version of the app to iOS devices without going through the App Store
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.