It is true in that scene that the stranger says, ‘Why would Dom have chosen to tell that story?’
That is an example of our signaling that there are people who wonder whether it was [a true story].
Your asking that question is very satisfying to me, because it makes me feel like the scene fulfilled its purpose, which was to do just that: to make people wonder whether he told the truth or whether, in fact, he did not.
People can interpret it as either, ‘Was it the right time to tell the true story?’ or ‘Was he choosing to tell a story that was, in fact, not true?’