I used to work in games, and the approvals for Nintendo, Sony, and Microsoft were all super, ridiculously frustrating at times. We had experiences very much along the same lines of failing again for doing the very thing they asked of us in the previous rejection.
Anyway, usually it works out eventually. No problem with making some noise about it being bad, and hopefully they hear it, but it is not uncommon, nor unique to Amazon.
The point about registering a URL isn't entirely accurate, IMO; plenty of Apple App Store apps consist partially or entirely of webviews. Even for fully native apps, Apple doesn't really have "control" of the code in the sense described in the article. Registration and the approval process are primarily there to give the publishers control over what appears in their store, as well as identify the submitters in a way that attempts to keep a little bit of accountability should they do something bad. Those reasons for requiring registration and review are just as valid for a url as for a bundle of code.