Salesman is being quite honest with you. Maybe a touch conservative but not much.
The manual states straight up 5000lb limit, so 7600lb dry is already way over before putting anything in the trailer.
Even 5000lb is going to be marginal due to payload of only 1600lb. At 5000lb fully loaded, you are looking at around 700lb hitch weight, plus the 3 of you (wild guess...400lb). That leaves only 500lb for everything else in the truck including anything bolt on like running boards, bed cover, etc....
If you get the 7600lb trailer, you are probably looking at 9000-10000 when loaded with a hitch weight on the order of 1200-1400lb.
Payload is going to be a major limitation and 1600lb is towards the low end of 1/2 ton pickup payloads. Figure 12-15% of the GVWR (ignore the empty weight as you won't travel empty) when looking and don't forget all the stuff already in the truck plus passengers.
