I don't quite know how one goes about proving a negative. But Indian Country has been on Churchill's case for years and this article by Suzan Harjo is a good summary of their semi-official view.
Plus, there are hearsay reports included that, at one time, Churchill claimed no Native American ancestry.
Another Indian Country article identified Churchill's supposed Cherokee ancestor as a gentleman named Tyner (or Tyson, can't recall), c. 1780-1800. It appears that Tyner's second wife was indian, but Churchill is descended via the first wife. A search of their website or Google might uncover that specific report.
thanx again okie01.
I used your references and commentary in an email to perkins. i cited you in my blog about it. u can check it out here
http://harkonnendog.blogspot.com/2005/02/another-email-to-prof-perkinson.html
if u like.