It's almost impossible to say exactly what proxy would cause that, as a lot of them do it. I have a pair of BlueCoat ProxySG devices in my office that do exactly what you're seeing above, and have the same end behavior.
What's happening is the proxy is requiring the user be authenticated to use the service. The request by the client is being sent, and you see it in the logs, but the proxy intercepts the response, and sends a message to the client saying that it has to redirect to a different page. That page is where the client/end user is supposed to enter credentials to login. A lot of times, especially when setup as a transparent proxy configuration, this authentication ties in with some network authentication, like NTLM, Kerberos or the likes. With the proxy being considered a trusted host as it is in the private network, most browsers can auto-send login information.
Once authenticated, the proxy server will most likely send back some cookie, and allow access to the original URL. As you can see from the HTML code you have above, there is an argument being passed to the authentication script called "original_url". This is so the page knows where to send the client.
If this is device is not on your network, and managed by somebody else, you should try talking with the folks that manage the network there, and discuss the possibilities of a special bypass for your application, or site.