I'm not sure why being connected to a router has anything to do with entering a call from the Phone port to the Line port in the Call History. The device is not connected to a network ?
The OBi110 obviously detects the ring and CID, as it has decided to not ring the Phone port, so I don 't see why it can't put an entry in the Call History. There is an entry in the Call History if I answer the phone ?