To the OP - somebody must have been pulling your leg. If you're convinced not, you might want to think about using a different dealer.
In the past we've always towed with empty FW tanks unless we knew there wouldn't be drinking water at our destination.
Someone above mentioned something about emergencies. We towed way more this year with the new trailer than we have in the past several years and having a bathroom a minute away from the driver's seat at any time was quite a convenience. I think, I am going to start towing always with at least a partial tank all the time, swishing or not.
Our FW tank is behind the axles so I can play around with the hitch weight if I want, although the rig seemed to run pretty well with the tank full.