No, they are not on the same switch.
I had this problem for a bit and I can only explain it for now but I will get some pictures for you sometime tonight.
There is a rod that runs along the left side of the steering column that controls your brights. It is actuated when you pull the "multi function switch" lever toward you. Unfortunately, this rod is not positively engaged by the multi function switch; There is a plastic piece that goes between the rod and the switch and if it isn't placed exactly right, it won't work.
I had the exact same problem on mine.
The temporary solution is to remove the plastic cover that is just down the column from the multi function switch lever (it is a complete PITA to remove) and find the rod that I am referring to. push that rod along the axis of the column and let it return. Your brights should turn off.
Like I said, I will get some pictures of what I am talking about tonight and update this post with those.