Your tires are "P" (passenger) rated. What the other poster was saying is that "LT" tires may be a better choice for towing. P rated tires have softer sidewalls for rider comfort while the LT tires are stiffer and won't flex as much with a load on them. You might make your truck a better tow vehicle but my opinion is that it is overmatched by your TT. We started towing our 2003 Pioneer 19T4 with a '99 Mountaineer. It got us to the campground but it was white knuckle at times despite having LT tires, super springs and a weight distributing hitch and sway control. Traded it for a '99 F250 Superduty and towing became much easier even after we ugraded to a much larger TT later. Proper setup is a must!
PS what the salesperson told you is the first thing they teach all RV salespeople to say regardless of the type of vehicle.