Does the App Store explicitly disallow bundling the source code inside the app? What if you added a .zip with the source into the app, and on app startup you copy the .zip out of the Application directory into the app's Document folder, which is accessible via iTunes (as long as you set the appropriate flag in the app descriptor plist to enable document sharing)
Bundling of source code with binaries is not required under the GPL. You can have it on your website. However the App Store EULA etc. are incompatible with the GPL (cf. http://news.ycombinator.com/item?id=3489115)
"You may not copy (except as expressly permitted by this license and the Usage Rules), decompile, reverse engineer, disassemble, attempt to derive the source code of, modify, or create derivative works of the Licensed Application, any updates, or any part thereof (except as and only to the extent any foregoing restriction is prohibited by applicable law or to the extent as may be permitted by the licensing terms governing use of any open sourced components included with the Licensed Application)"
I assume this is what makes the LGPL okay to use? (LGPL explicitly requires allowing reverse engineering of the entire application, even the non-LGPL parts)
(I don't know much about iOS development, so will take your word that this is the standard licence that software on the AppStore goes to the customer under)
There are numerous parts of that licence that are incompatible with the GPL and other Free Software/Open Source licences:
e.g.:
This license does not allow You to use the Licensed Application on any iPod touch or iPhone that You do not own or control, and You may not distribute or make the Licensed Application available over a network where it could be used by multiple devices at the same time. You may not rent, lease, lend, sell, redistribute or sublicense the Licensed Application.
If $COMPANY (e.g. Canonical gives me a Linux kernel) gives me a piece of GPL software, I am allowed to install that on numerous devices, I am allowed to sell that software myself and keep all the money myself, I am allowed to install that software on my friend's computer. All of these actions are prohibited by that Apple Licence, and hence in order for Apple to give/sell me a GPL programme they would have to change that.
Apple have chosen to get around this situation by not giving me any GPL licenced software.