I found the issue that was making the WebUI wrongly believe my STV was remote. The "EasyPrivacy" filter set for AdBlockPlus was blocking the "/ping.gif" element on the STV web interface. Adding an exception rule to the AdBlockPlus filters resolves the problem. I'm not sure if this is a newly added rule to EasyPrivacy, or if the STV WebUI changed.
Here's the exception rule I've used. This will disable AdBlockPlus on all simple.tv webpages. Hopefully this will be helpful for other users.
Every few seconds, the WebGUI fetches the file "ping.gig" from the IP address of your locally connected STV. If the transfer succeeds, you see the Home Icon. If it fails, you get the round remote ICON.
To the original posted rowbert: If an STV box on both your local and remote networks have the same IP address, it's possible that this could confuse the WebUI into wrongly believing a remote STV is local. Let's say that both have an IP address of 192.168.1.101, the UI will try to fetch "http://192.168.1.101...tic/ping.gif?_=(Number Goes here)". This would normally fail, but if both networks have a box at that IP address answering the response it may wrongly believe it to be on the local network.