I can't speak for the Anderson hitch since I run an Equalizer, but do have experience with the OEM Suburban hitch. I never noticed any issues when I had our Jayco hybrid which was much much lighter. Our new Cougar has a loaded tongue weight north of 1000lbs. I noticed after initially adjusting the WD bars for the new trailer I had a troubling amount of flex from the GM hitch. When the WD bars were loaded, the pin box was obviously not vertical, but tilted up a troubling amount. Would it have failed? I was not going to risk it. My hitch honestly looked to be in great condition with almost no rust but I installed a Reese Titan any way. In addition to being a stronger hitch, the mounting bars are almost twice as long as the OEM hitch. This will distribute forces over more of the frame which will also increase strength. After spending $25000 on a new trailer.... a $300 hitch was cheap insurance.
Also, after installing the Titan I had no more pin box flex. I am not sure how GM felt comfortable putting a 1200LB rating on this hitch. Sorry for the long rant but I just went through this two weeks ago so it is still fresh in my head!
Best of luck to you!