No, Kakashi didn't state that they were. He said its "believed" that the sharingan descended from the byakugan. In other words, its an assumption in the Naruto world. I suppose at one point in Narutoverse history, the sharingan and the byakugan had similar characteristics, but then they evolved into the current representations of each.
Originally Posted by Shock
And there's most definitely a medical jutsu behind the transplant of eyes.