If he bought the truck new, the truck should have come with the 2 inch sleeve so his 2 1/2 inch receiver can accept a 2 inch shank. So, I hope he did not have to pay for that. Anyways, I have near the same set-up and did not like the slop so I bought a hitch with a 2 1/2 inch shank. If nothing else, for peace of mind. As far as the slight downward tilt, that should be right. So when the trailer is placed on the hitch and raised up to attach the distribution bars, the trailer is lowered back down for a level set-up to include the hitch head itself. There should be some type of adjustment on the distribution hitch head so a level set-up can be achieved once the trailer it attached and bars in place.
If the trailer is attached and distribution bars are in place and the hitch head has a downward tilt, he needs to do some adjustment.