I made a previous thread that hinted at the Sarutobi and possibly most, if not all, clans under the class of Senju or Uchiha: http://www.narutobase.net/forums/sho...d.php?t=286527
Building upon this theory, I looked deeper into Kakashi Hatake, and this thought came up, "Is the Hatake clan also Senju under this presumption?"
I found this interesting manga page that might be addressing a correlation, and may explain why Kakashi is able to use the Sharingan:
Now we know that when we talk about Senju's we mostly address their bodies, and here Kakashi's body is "Suitable" according to Itachi, to accommodate the Sharingan, though not perfectly.
In other places we see Sharingan users being able to accommodate Senju DNA too: