How to authenticate docker hub api request?
So after a few more hours of working on this problem, I came across someone who had similar issues and wrote a blog post about exactly how to solve it. The short answer is the endpoint that was missing from the docker api documentation is https://cdn-registry-1.docker.io/v1/. Why didn't they document their api better? I don't know. If anyone wants to read the full article about how this is done, you can find it at http://www.appcontainers.com/requesting-image-information-using-the-public-docker-api/
This was the most helpful article I have found on the subject. Hopefully this will help some other poor soul who is trapped in the confusion known as the docker api.