I don't think it's the car wash. I'm almost positive it's the finish.
Just to add, my running board has another problem beside staining.
I was stepping on it for an extended period to install a roof rack and when I was cleaning the foot marks, I noticed that the black rubber dimples were sinking. If you look closely, the rubber part comes loose and you can actually push it down. I don't think this is normal since the rubber part is there for safety reason and it would not server it's purpose if they all come loose and sink on the board. My dealer will be replacing them this weekend.
I think the entire design and quality of the running board is pure crap.