Who is "they"? The sales guys? I would expect even the lowest rated 2500HD can tow that trailer within all specs and be fine. Comfort you'll have to judge on your own as experience with towing a big trailer like that goes a long way towards how you feel.
I did just buy a new truck 2 weeks ago, but prior to that I was towing my 2019 330RSTS with a 2017 F250 6.2L gasser. I used a SwayPro hitch and added airbags to help with squat, but otherwise I never felt uncomfortable. In 2018 we took a 3500 mile trip out west, over the Rockies and down through Utah. Never felt uncomfortable in winds or when trucks flew past us. It was slow going through the mountain passes and used an insane amount of gas, but otherwise I enjoyed pulling that beast trailer more than pulling my old pop-up with a Yukon.
I'm guessing you'll weigh in similar to me. On the scale, my 330RSTS is 11,300lbs loaded and ready for camping. Hitch weight came in at 1,600lbs. Assume worst case you hit the GVWR of the camper at 12,000lbs and push 1,800lbs on tongue weight (15%), are you within your towing capacity, payload rating and hitch rating?
2000 FR Flagstaff 625D - Sold
2013 White Hawk 30DSRE - Sold
2019 Eagle 330RSTS
2020 F350 Lariat 6.7L powerstroke, Rapid Red with Lariat Sport