Ethernet rejects induced hum from external wiring due to the twisted pair nature. Hum as a point to point potential between the interconnected devices is not so well rejected. That's the mode I always see when I do run into hum problems with it. It's a problem that can't be 100% eliminated short of running everything on DC. But the higher the voltage between equipment, the greater it can be. A pair of ungrounded 208V systems could have the effect of a 416V system, depending on the phase angles and other aspects at the time. Grounding the 208V systems on one end would prevent it being like 416V. Grounding on the center tap would be even better. There are other ways to mitigate the problem, too, but grounding the power system is one of them.

There's also the risk that the ungrounded system can exhibit higher differential voltage in a surge than an ungrounded system. This can be mitigated by additional surge protection to help maintain the voltage equality (e.g. clamping the 208V system into ground, during the transient).

Here are two different UPSes. The first appears to be a single ungrounded-output inverter. The second (more costly) appears to be grounded.

http://www.apcc.com/products/resource/include/techspec_index.cfm?base_sku=SURTD5000RMXLT3U

http://www.apcc.com/products/resource/include/techspec_index.cfm?base_sku=SURTD5000RMXLP3U