Its good that you are not trusting the sales person. Some are pretty honest and savvy when it comes to towing. Most are not.
The short answer to this is that, yes, you can tow a trailer with an overall weight of 4000-4500# without any problems. Keep in mind that the 4500# is considering that would be its GVWR, not "dry" weight. In other words its maximum weight that it can be fully loaded.
If the 4500# is the listed dry weight, then you may be pushing it if not over weight. Dry weight is a fictional number. Dry weight is the weight of the trailer before any options are installed, and before any propane tanks or battery is added. A trailer never even leaves the factory weighing its dry weight. And no one tows a trailer that weighs its dry weight.
Also you didn't tell us what year, motor, and gear set your 'Burb has. All of those specs are important because the various towing related numbers change with model years, engine sizes, and gearing.
EDIT: Also, is this a C1500 or a K1500? Usually 4wd drops towing capacity by 500#