Stories can be conceptually true, even if they’re factually inaccurate. James Frey pretty much argued that A Million Little Pieces was true on this level.
Statements or pictures that are factually untrue can be true to the “spirit” of what is being conveyed. A couple of years ago an advertising campaign was criticised for promoting the Costa Brava using a photo that was actually taken in the Bahamas. In its defence, the tourist board said: “What we were looking for was the concept (…) We absolutely didn’t think we were betraying the spirit and the promotion of the Costa Brava, which is what interested us.”
On the other hand, stories can seem authentic even if they’re not. So-called reality TV shows sometimes re-shoot scenes if they didn’t work quite right the first time. We also know that shows like The Hills tell stories that seem real even though they’re at least partially made up. Yann Martel’s Self seems like an authentic autobiography then reveals that it can’t be.
I think we look for signs of authenticity before deciding whether or not to believe a story – but those signs can be misleading. This is one of the problems with our tendency to make a binary distinction between truth and falsehood.