I think this problem has something to do with cached authentication. On a laptop that is unable to get a list of applications from webfeed.aspx, I created a new user, which was able to get a list of applications from webfeed.aspx, using the same RD user.
I have no idea where this authentication is cached. I deleted all my web browser cache and I deleted all the credentials in the Credential Manager. Still no success.
The way RD gets it's list of applications seems to be this black hole of non-standard implementation. There are no event logs for this failure. It uses cookie-based credentials that don't expire, but it doesn't actually use the cookies to persist the ticket and it doesn't store the credentials in the Credential Manager.