Anecdata: I bought a Toshiba 55M550KU a month or so ago. I've never plugged it into my wired network, and didn't give it my WiFi password. Yes, the main menu is focused around all the things I could do with Internet access, but all I have to do is choose "inputs" and I can configure it as I like with no "CONNECTION REQUIRED" barriers. This means I've never updated the firmware, but I'm guessing those updates would mostly benefit the complex (and changing) apps that I don't use.
