NLA uses the MAC address of the user's DSL or cable modem as the link
ID.
Source
To get the public/private option to show in the GUI windows needs to identify the network via the NLA service. To achieve that the network adapter connected to the network needs to have a default gateway.
Windows's NLA service will then identify the network by the MAC address of the device entered as default gateway. It doesn't have to be a a router, but there must be a device/MAC under that IP otherwise windows will keep trying to identify the network.
