For a narrative to resonate effectively, it must be both credible and coherent. This means that it must be presented in a fashion such that it is trustworthy and believable and it must be consistent internally as well as with external information and reference narratives available to its audience.
It does not follow that a narrative has to be true. A fictional narrative can convey reference information that can help people navigate uncertainty. Narratives, after all, generate real-world effects; as well, the kinds of small-world models used by economists to explicate large-world matters are themselves narratives.
Rather than referring to narratives as true or false, we should look to understand them as useful or not.