Microsoft doesn’t have access to the APIs, that doesn’t mean they can’t reverse engineer access (it’s fairly easy to do). But that’s against the terms of service.
So Microsoft built the app, reverse engineered the APIs they needed, and then deliberately stopped the ads from playing and added downloads. So Google came out and attacked the downloading and ad issue specifically.
That allows Microsoft to back down, add the ads in, disable downloading, and then gets a Youtube app in the store where Google wouldn’t allow it before.