I bought a new 03 Expedition for $60k and it had a shimmy in the steering wheel. First thing we did was rotate the tires to see if it moved around. Could just be a wheel out of balance or a bad tire or a rim out of round. My point is, it happens to all of them.
My fix was to replace the tires. Not a great solution on a new truck but I love michelins and I don't like cheap tires ruining my vehicle experience. btw, the first stop I made when I picked up my new ram was to my tire dealer, he have me $70 each for the sh*t wranglers and now I'm thrilled with a set of michelins on it.