Weight distribution hitch needed?

We pick up our first TT this Saturday! We've bought a 2015 Palomini 179 BHS (3839 GVWR) and will tow it with a Toyota Tundra SR5 truck (tows 10,000 lbs). The dealer says no weight distribution hitch or sway bar for our truck/camper combo. I'm inclined to believe him since they sell both. It's hard to fathom a salesman who doesn't want that extra bit of money.

What do you think? Are we crazy if we don't get a weight distribution hitch or sway bar? Or would they just be overkill?

Thanks for any input!