An article in the The Daily Jeffersonian of Cambridge, Ohio, November 19, 2012
Linked to Lincoln DNA confirms local man descendant of 16th President illustrates how misleading such stories can be.
According to the headline the man is a descendant of the President. The story makes it clear he's thought to be a relative, a descendant of President Lincoln's half-brother.
The article indicates the man took a DNA test with Family Tree DNA and "The results provided the confirmation he needed: His branch grew from the Lincoln/Linkhorn family tree." A bit more information would have been helpful. There is a Lincoln DNA project with several good Y DNA test results for descendants of the three Lincoln brothers from Hingham, Norfolk, who moved to America. Samuel the weaver was President Lincoln's ancestor and the descendants are all haplogroup R1b1a2 (shared by 60% of the men in Great Britain).