This has been bothering my for awhile. Yes i agree an expander button is a common cause of runout, it's purpose (in my head at least) is not really to smooth dings out but to size the only thing we really care about, the INSIDE of the case neck, as that is where the bullet's going.
Because brass thickness varies, you pick a bushing that sizes the outside of the neck down enough to ensure it's a touch more than required on all of your same headstamp brass. The button will then open any that need it so that your NT is relatively consistent (not including spring back, thickness, annealing differences, etc)
I think the runout problem is not the button, it's that you are pulling on a case that is not held the best way aka a shell holder. If the expander button was actually round, not having any flat spots, it may help with pulling the neck off to one side. The one i have has a flat on it.
I don't use a button for the reasons above on brass sized with a bushing but i do use an expanding mandrel for the same reasons but get much straighter ammo since i am pushing on the case versus pulling when expanding.
All this thinking may be completely wrong, so critique away.