I tow a trailer behind my trail-a-bike, but it's a different model and attaches to the bike using a very sturdy bracket that attaches to the seat post. The design of the Burley is just...odd, IMO. Knowing the size screws used for rear racks, yeah, I could see not recommending adding a trailer. By contrast, the fasteners for my trail a bike are easily 3x thicker. I don't exactly know what the shear strength on them is (not an engineer) but I could see overloading being a problem.
Keep in mind even a super durable rear rack is usually only rated for 75-100 pounds. The trail a bike plus a child is easily that already - hence no extra weight.
The "install by professional" just sounds like standard CYA boilerplate.