Do you know of any reason why a yellow rose bush, that I cut down all the way (I left the root), would grow back with red roses?

Your rose may have been grafted. A grafted or budded plant is one in which a small piece of the desired flowering variety (the scion) was surgically attached to a root system from another rose (the rootstock, understock, or just "stock"). These two parts heal together, to become a single plant. However, if a grafted plant freezes to the graft union, or in your case cut back to that union the rootstock may sprout out, but you will have lost the original grafted variety and have a totally different rose.