"I'm not sure that the it's relevant that some people don't believe a story, or that they call it a "fabrication." The question, is, what is the integrity of the story itself? Is it true to its intended purpose?"
You have moved the goalposts of truth there considerably, I think. Yes, a story, even if totally fabricated, can have moral integrity. But we now have an extra layer of potential weakness that isn't there in the case of an historically-accurate account. We have a human being telling a story, not just relating facts, and this person may have agendas we can't detect. The story may well fit into our moral framework (most of what Jesus allegedly said will do me very nicely) and the fabrication may have been that of a very wise man or woman. But, as you give away, unlike an neutral, historically-accurate account, it has "an intended purpose". We are edging away from truth ever so slightly. I suppose that most historically-accurate accounts are also made by people, but at least we can grill them for evidence. I'll never let religion make me think that evidence is a dirty word!