BTagent in the firmware if installed can instigate a remote modem reboot i.e when automatically upgrading firmware.
i see where you are coming from , however this firmware has the btagent removed ( unless it can access some other way)
however , i found this in the router logs...
"Couldn't get channel number: Transport endpoint is not connected" , and on checking google it seems one customer had a short in the cable going to the pole causing the disconnects and was getting the same message.
if its of any value though, it seems he was using the same router as me , a billion 7800n with firmware 1.06h.