Rackspace Cloudfiles publicly accessible Origin URL?

When using Rackspace Cloudfiles, and having Akamai CDN distribution enabled, a typical download http (publicly accessible) URL for a file is something like this:

http://7c3ca13c7a3lkld0f0ae5-83a5b57cdllakjeidk39d8.r36.cf2.rackcdn.com/css/style.css

But according to the API (and tools like Cyberduck), files have an Origin URL as well. Usually something sort of like this:

https://storage3kd.ord1.clouddrive.com/v1/MossoCloudFS_ra6c36-e36d-45c9/dist/css/style.css

When trying to access the Origin URL in the browser, I get an Unauthorized message. Is it possible to make a file publicly/anonymously accessible via it's Origin URL?

With Amazon AWS S3 + CloudFront, you can set it up so you can access a file either through it's cached CDN URL or via it's uncached S3 Origin Bucket URL.

Can you do the same thing with Rackspace Cloudfiles? If so, how?