That response is a little confusing: the management app is Internet only, but it doesn't drop all its routing tables or something just because the uplink is gone. Moreover, the regular DHCP and so on will operate just fine while not connected to the internet.
I don't know what happened in your case and I totally agree that it's a bad experience for troubleshooting (the thing even has some weird API on it [1], so why isn't there some basic web-based management tool), but you can absolutely unplug the uplink and packets flow locally.
