This writer (and I'll bet you his doctorate isn't in history) treats everything from scurrilous campaign trash to wild speculation as gospel.
With that said, there's a pretty good chance that one of Harding's great-grandparents was black.
The Four Mysteries of Warren Harding. A good article from American Heritage by Francis Russell. The good doctor misquotes from this very article, apparently (it was not "Republican officials"):
Whatever Harding’s frustrations and anger at these mocking accusations, he always followed the manly course of disregarding the rumors about his heredity. He himself did not know whether they were true or not. “How do I know, Jim?” he once told his old friend James Faulkner of the Cincinnati Enquirer. “One of my ancestors may have jumped the fence.” Nor, in a day when such matters have come to be of less concern, is there anything more to add to that honest comment.
While visiting the Harding house in Marion last year, I saw the pictures of his grandparents hanging in the hallway on the second floor. Looking at the one picture, one could only conclude that his paternal grandfather was black.