Almost any combination can benefit from a properly adjusted anti-sway device. You are "way over-rated" for the towing of your trailer, that is probably why the dealer said you didn't need one. But...
You are over-rated with your tow vehicle only on the ability to absorb tongue weight. You are not immune to sway and, may indeed, be more susceptible to it. You have a big heavy truck, heavy, stiff springs and next to no "felt towing" with that size trailer. Your springs will cause more up and down see-sawing of the tongue since the tongue won't weigh enough to load those HD spring packs down. What that means is that the trailer is going to flail about behind your truck and you won't notice it until too late. The trailer, being lightweight, is actually more prone to the forces that cause sway; it doesn't weigh much, won't have much in the way of tongue weight, but, still has the "sail area" of an RV. Much akin to an unloaded utility trailer bouncing and swaying around behind the tow vehicle; we've all seen it going down the road, but, your trailer will have enough weight to eventually cause a handling problem and most likely when you can least afford to have an issue.
While you won't need a weight distribution hitch (having one though, won't hurt in case you trade up later), but, you will still benefit from an anti-sway device. Whether it is part of a weight distribution system like the Equal-i-zer or Reese or a standalone anti-sway friction rod, the choice would be up to you, but, I'd recommend the anti-sway friction rod as a bare minimum.
My 2 cents, your mileage may vary...
2 Cats; J-Lo and Ragamuffin :R
2014 Thor Tuscany 40RX DP
2011 Ram 2500 Longhorn CTD HO
2011 Keystone Cougar 318SAB (now gone)
2008 FunFinder X 210WBS (Sadly gone)