On the other hand, a Google product (YouTube) is asking for permission to access information already available to another Google product (Android). If Google had no respect for your privacy, they wouldn't even ask.

Respect for privacy is a continuum and Google isn't on either extreme. I'd even go so far as to say that different parts of Google have different stances on privacy. People who try to make them into a monolith with a single binary stance on the issue are lacking nuance.