If the concrete were drawing the oil out of the tire, there would be an oily spot left on the concrete after the vehicle was driven away where each tire was. Have you ever seen that? I never have.
Flat spots come from having the weight sitting on one side of the tire, and happen regardless of the surface. Elevating them prevents that. Dry rot is mainly rubber aging due to heat, UV light, ozone, etc. Do you generally see tires where only a small bit of the tread is rotted (the part in contact with cement)? Or is it generally the whole tread, or the sidewall?