I routinely fill the tank at home ( yep all 30 gallons plus 6 in the hot water heater ) and travel 236 miles to my destination camping area.
No issues with my tank mounts, and the Pod is still barely half of the tow rating of my TV. The overhang from my rear TV axle to the tow ball is VERY short (a great thing) compared to most SUV's.My only beef is that the fresh water tank is mounted behind the axle, and unloads the tongue weight. I can notice a difference when towing, but it's not a big deal.
It wouldn't make sense for Forest River to have a tank mounting system that couldn't handle the extra weight of full tanks while transporting. The gray tank especially can become full during a camping trip, and when dry camping, you must tow to a dump station, wherever that may be. ( I live about 9 miles from a public dump station at a highway rest area here in CT, open from late Spring to Late Fall, free )