This is false. Betteredge himself confesses during this conversation that his thoughts were "muddled" until "Mr. Franklin took them in hand, and pointed out what they ought to see". Furthermore, wasn't it Franklin who pushed Betteredge to write his recollection in the first place? Franklin's influence on the Betteredge is apparent, putting into question the reliability of his narrative as well as Franklin's motives.
It again brings up the dichotomy of opinion versus fact, subjective versus objective. This reminds me of "In a Grove" by Ryunosuke Akutagawa, which was adapted into the film "Rashomon" by Akira Kurosawa. Very similar themes and narrative structure.