Well, we may never know the truth for sure, but I do have actual newspapers of the time with reports from the troops who captured him which says otherwise. Now they may have been lying, but they did give those accounts.
Davis had his faults, to be sure, but there is no need to disparage the courage of a Mexican War hero, who, on at least two occasions as President during the Civil War, had to be urged by his field generals to move farther away from the front lines for his own safety.
I would certainly call treason a fault. His courage does not make up for the catastrophe he and his criminal cohorts caused this Nation.
To avoid thread drift we should take this conversation elsewhere on FR, but I'll just say that neither Davis nor any other Confederate was ever tried for treason, even though the Andrew Johnson administration, Congress, and a majority of the U.S. public wanted to do just that.
There's a reason for that, and it wasn't Northern benevolence.