There is definitely a need for private APIs that normal apps cannot use - they might have security implications, for instance. The App Store or Settings apps clearly need to be able to do things that other apps cannot do - for instance, any app that had the same privileges as the App Store would be able to install/uninstall other apps.
Further, Apple's position is that the App Store, Settings etc. are akin to natural monopolies - it only ever makes sense to have one of each. The fact that it's not possible to implement a third-party Settings app isn't a problem because nobody should ever need to do this. This is arguable, but it's an easily defensible position for Apple and most iOS users would be happy with this (and those who aren't can jailbreak).
Having private APIs that are available to apps like iBooks, when competitors to iBooks exist, seems a bit shadier and much closer to the example of Microsoft Office using hidden/unpublished Windows APIs in the 90s. iBooks isn't some essential system service, and should be replaceable by a third-party app according to user preference. If Apple are making it even slightly more difficult for a third-party app to replace iBooks then this would appear to be anti-competitive.
IANAL, but I doubt that there is a legal case to answer. However, there does seem to be a moral case to answer. Sure, it's Apple's product and they can do what they like, but we have seen what happens when essential software vendors do what they like, and it's generally not pretty.