After wondering why it kept returning a 401 I finally figured out that the API quota was set to zero out of the box and that I had to fill out some form with a bunch of ridiculous questions like "what will be the impact to your business if your quota is not increased?" Uh, I won't be able to use the API at all because it's currently zero?
The end result was that it took about two weeks of back and forth with Google Support trying to make them understand what I was using the API for before they finally relented and increased the API quota to a non-zero value.
I get that Google is probably somewhat protective of the YouTube API and I'm just some Joe Blow looking to query it for non-revenue purposes, but if I were a business it would have been an insanely terrible experience to get set up with a third-party API.
Compared to every quota increase request on AWS which is either self-serve or something a support ticket handles in a few hours typically.