I am not a lawyer, but I'm pretty sure that just because the website (an online service) allows end users to download some music (provides a "download" button) it doesn't imply that other parties (you) are allowed to create software that utilise that button automatically. These are probably online services, with Web user interface, meant for end users, probably with some Terms of Service that these end users are obliged by. In my opinion, it's similar to a case when a web app has (private) REST API that is used by its frontend client. The fact that such a private API exists, doesn't imply that a third party can create and distribute software that uses that REST API. Technical possibility to do something does not mean that you can do that thing. In other words, I believe that Apple might be correct by saying that "[you lack] authorization from the relevant third-party sources". You assumed you don't need this authorization based on existence of "download" button, while that assumption might me incorrect.