Maybe back in its infancy towing with a CVT tranny would have been a concern. Fast forward many years and you'll be fine. Stick to the 5,000 lbs capacity published by Infiniti (I would even err slightly lower than that just to be conservative), but to generally state you shouldn't tow things with your QX60 these days seems just plain wrong. There was just another thread in here regarding both towing objects and also hauling things in the rear cargo area. Many members have done both with significant weight and have not had any issue with either suspension or transmission. I would consider that to be a non issue
I have a client who tows her camper with her QX60 and it works great. Usually I caution people about towing things that are much taller than their vehicle - on the freeway wind resistance is a bigger factor than weight. But her camper is pretty tall and still works great.