Switching the user agent isn't enough because it's not blindly relying on the user agent. It's actually doing feature detection so if your browser doesn't support whatever features used for remote desktop it'll give you an error message without relying on whitelisting a particular browser. This is exactly how web applications that need to use non-universal features should work, sure, look at the user agent for blacklisted browsers but use feature detection for what you can so that a new web browser that supports it will work without needing to modify the whitelisted user agents.
But switching the user-agent isn't enough in other browsers, Google must be using some fuckery in the background.