Tacito
I also just took delivery of an Elevation I found in my local dealer's inventory. Like you, I assumed that a receiver hitch was also standard equipment on the truck. The one I bought did not have the tow package on it, but when I looked under the rear bumper there appeared to be an actual hitch assembly minus the 2" receiver tube. Instead, it had hole in the assembly that lined up perfectly with a hidden hole in the bumper above. Like previously said, a hitch ball could have been installed, but I really didn't want this. I also noted a sticker on the that hitch assembly was rated at 3500 lbs.
I negotiated with my dealer and he ordered the hitch and wiring harness from the GM accessory warehouse with me paying for the parts (at cost, I doubt it) and they installing for free. This was just last week and the parts came right in. I'm not worried about pulling the max or taxing the cooling system because I only short haul a 2000 lb "honey do" trailer for my wife for mulch and stuff. I've got to get my 500 miles on the truck before I next pull the trailer. My dealer had suggested using a local hidden hitch dealer or the like, but I wanted factory parts and the warranty that comes with it.
FYI, ordering accessories for the truck from accessories.gmc.com was quick and easy. There are discount codes based on how much you are spending and the parts shipped to the dealer were there in two days. As previously stated, on some accessories there is even an option to pay for installation at check out. Highly recommend it. Hope all works well for you.