Ethernet by definition isn't a grounded protocol. if you attempt to ground one end, you're going to fundamentally screw up 0 detection on the other. Both ends need to know where 0 is, and this is achieved by using a floating ground. Granted, since we're talking Ethernet anyway, any ground would be an earth ground and relatively close to each other. That statement is literally non-sense. You'd never use an earth ground on one side and a floating ground on the other. You never ground on one side and not the other. Plus, a "ground loop"? What the hell are you talking about? Ground is where 0 voltage is defined. To imply a loop, that would mean 0 on one side was connected to something other than 0 on the other, which would lead to a feed back loop which would cause all electronics connected to it to let the magic smoke out. You'd burn everything out if you tried to do such a thing. If you're concerned about grounding non-connected items, you use an earth ground, as it's a constant and not relative. As a power engineer I literally have no idea what you're talking about. You want all grounds in the system to be tied to a constant voltage. It doesn't matter what that voltage is, just as long as it's constant across all connected nodes. if they're not all connected and you want different ground voltages, then you have to use electric isolation, usually in the form of either magnetic or optical isolation. But Ethernet doesn't support either of those.
Ethernet is transformer isolated on both ends but if a shielded cable is used, then the shield connects to chassis ground on both ends. The problem occurs when chassis ground at each end differs which is not uncommon when dealing with the distances that long lengths of cable allow.
If a current flows through the shield then it couples to the ethernet signal lines but this would be unlikely to affect ethernet. When dealing with audio gear or sensitive instrumentation however, the ground current can cause problems whether it affects the ethernet interface or not and the common solution is to use an unshielded cable or ground the cable at only one end.
Professional audio gear uses balanced instead of single ended connections for audio to prevent ground loops; this is just an extension of that. It is also why USB and Firewire and not suitable in many cases unless a galvanically isolated interface is used.