The point being here is yes you can use 2x4's but you really need to line the entire bed floor with 2x4's, or add a sheet of plywood, to make sure you are supporting the camper properly.
Campers usually have a thin outer skin with a skeleton structure hidden underneath for the floor. The thin skin will not support the weight of the camper.
On a smooth bed with no rails, the entire floor of the camper makes contact with the floor of the truck so it does not matter where the skeleton structure is. It will always be 100% supported by the floor of the bed.
With 2x4's at random intervals, you are depending on random chance that the 2x4's will line up with the skeleton structure of the camper. Odds are it won't. The camper will only be supported by the outer edges, and its own weight coupled with bouncing down the road may cause the 2x4 to push up into/through the thin floor skin, possibly damaging the camper.
Risk of damage may or may not be small. We don't know. But, since it's so easy to go from possibly-low risk to absolutely ZERO risk, by simply adding a sheet of plywood, it would be foolish to not go ahead and do it.