Being slightly paranoid, I wish to use a Ethernet surge protector to protect the Coax->Modem->Ethernet side of my computer network if there is a surge on the Coax line. Almost all of these ethernet surge protectors have a pigtail that you are supposed to hook up to ground, and APC demonstrates this by using the computer case the ethernet cable is being plugged into as the ground. An example image here:
My question is, if the mains power powering the computer is going through a surge protector, should this still be grounded to the case (or any other ground point past the surge protector), or should it be grounded directly to ground?