In the case of the App Store, Apple is the one doing distribution, so Apple must also comply with the terms of the license (in addition to the app developer). Apple has decided they will not do that (that is, people they distribute to will not have the ability to modify the LGPL code, relink the final executable, and run it on their devices), so Apple cannot legally distribute binaries that contain LGPL code.
It only makes sense, then, that Apple should preemptively reject apps that link in LGPL code, as they know that they will not abide by the licensing terms.
> If I have the OK from Tim Cook and all the secret signing keys, I can compile and run anything I want on my iOS device. And even without that, if somebody provides all the object files of non-LGPL code and build instructions, I can replace the LGPL code and run my own version outside of the app store.
That's not permitted by the license. The (L)GPL prohibits a third party from adding extra conditions to exercising the rights granted in the license. "Pay Apple for a developer account and get their permission" is an extra condition. Even if there is a jailbreak-y method of getting around the extra conditions, I don't think that would fly.
> Often when people ban (L)GPL code, its just a pretext, because they don't want to deal with the complexities or for other reasons.
Agreed, but I'm not convinced this is one of those cases.
