On machines that are connected to private LANs without internet access, the plasma network systray icon shows an exclamation mark. This indicates something is wrong even though the machine is not expected to have access to Internet.

On Windows, there are means to disable the internet access check and prevent such status icons. But I can't find any straightforward way on Plasms, other than meddling with the icon files. I feel this is a genuine requirement as having a network connection does not mean it has to have internet access.