The truth is always the strongest argument.

A true account needs no maintenance. Anything else has to be remembered, kept consistent, and defended against the next detail that surfaces, and that upkeep is what eventually gives it away. Truth stays where you left it, which is why it outlasts cleverer versions.

In the disagreement you are carrying, try saying the plain thing first, before the framing. It will feel thinner than the polished version and it will hold up better. If you would rather not give the plain account at all, that is information about the situation rather than about honesty.