You should thank your lucky stars for all the people who buy Wranglers despite not using them to the Jeep's full capabilities. It probably wouldn't exist without those purchases.
I had the original sideplates on my 1Up with a standard hitch and it folded up fine on my Sahara with Rubicon wheels and KO2 33" tires. When I went to a LOD rear bumper with a built in hitch I had to run a drop hitch until I had custom sideplates made at a local machine shop, since 1Up refused...
He's referring to getting an aftermarket differential cover. Literally replace the entire half with the fill plug of the differential "pumpkin". They can be much heavier duty than the stock ones, and some allow it to hold more fluid.
I have a Sahara. No issues when I had stock bumper and hitch. I noticed one of the pictures above, he has the tongue buried in the hitch. It doesn't need to go in that far and would give him plenty of room to fold the rack up when he's not carrying bikes.