First, I'm no expert. I have a cable modem connection and my activity lite is constantly flashing when sitting at a desktop. I see this as normal. Even when Firefox or anything similar is not open. I think it is just normal procedure for a network system to periodically send and receive basic signals, like 'keep alive' when it is up and running. Maybe a live distro doesn't operate quite the same way. I'm more interested in watching my network activity reported in Conky. If I see more than a few hundred bytes per second download, something is not normal when all apps are closed. I really think this is just normal working network activity.
i5 3570k, ASRock z77 Extreme 4, 8 Gb Ripjaws 1600, Antec 430w psu, HVR 1600 tv tuner, custom case- marble top, oak face. Carver & DCM Time Window sound system. Mint 14 KDE.