Tire Load capacity on 20" rims/tires when towing car trailer?

So I went to the local rental store to rent an open top car trailer and the owner would not rent to me because he side my tires....Stock 265/50R20 were only rated at 2140 lbs each and they must be at 2500lbs. The weight of the car, 3200lbs and the trailer, 1800lbs is 5000lbs. So that was last year and I just borrowed my neighbors truck. Now I am purchasing new tires at 30000 miles and wanted to get some that are rated at 2500lbs.

Any suggestions on tires? I would like to stay with stock size.

Is that tire load weight an issue for towing the car trailer?

Finally, why would FCA spec the JGC with these tires, say it can tow north of 7000lbs, but the rental stores will not rent for safety reasons.

Looking for some feedback.
Thank you.