Of Lincoln I am sure the story is blatantly mendacious revisionism.
Concerning Mr. Jefferson, I feel certain it is the truth because it happened in my family.
I first realized it was possible when I put a photograph of my father next to the very prominent Black person that has the same surname as my family. There was a very strong resemblance and I have learned just this year on a family genealogy website, it has been confirmed through DNA testing. By a strange coincidence, one of my colonial relatives owned property adjoining Thomas Jefferson's. I suspect, in early Augusta County, Virginia, the practice was more common than many would like to believe.
Some recent scholarship on the Jefferson-Hemmings relationship points to Thomas Jefferson's nephew, who lived near Monticello and was a frequent guest there, as the most likely father of the Sally Hemmings children usually attributed to Thomas Jefferson.