Exactly my thought: why have one server proxy request to another Web server instead of having the client use the API directly?

Your main Web server could just serve the initial page / application / whatever, and then the application lives on the client, fetching data from the API and formatting it as needed. You end up with proper MVC in the browser.

That's what I did for a small side-project of mine last week and it worked very well. I detailed how I built it here: https://plus.google.com/118077068834135870002/posts/62agb7qp...