It of course depends on the nature of the story. Putting that aside for a second, the story is probably being made into a film already because there is the promise of a good narrative to be found. I love how films like Redford's Quiz Show, Mann's The Insider, or more recent films like Fincher's The Social Network or Hanson's Too Big to Fail, take situations that in reality aren't as compelling as they perhaps should be and turn them into watchable scenarios. Things always need to be changed for the screen. This even holds true for adaptations of novels, plays, etc. I think the filmmaker should look at the truth and then as they go over it, decide what is true in spirit to tell their story.
I mentioned the nature of the story, and you have popular films from last year like Boyle's 127 Hours or O. Russell's The Fighter that showcase characters who aren't in the happiest of places. Aron Ralston and Micky Ward supported the films. I think when your subject is alive and the publicist/the agent/themselves are supportive- then you have a responsibility to consult with them and have them aware of your approach. Their story may be widely known or already published in another format- so if they've opened their heart up to the world then I'm sure you can approach them like you would approach an actor playing them.
If the subject isn't supportive and at the risk of sounding too hypocritical, well then Fincher's film is a great example. It takes events mentioned in a book and creates a character named Mark who goes through an emotional arc. Someone correct me if I'm wrong, but no one ever said this is Facebook: The Movie, it's a dramatized story. This is how I personally feel, I realize that when you claim a film is based on truth, the mass audience probably expects the truth, but that is where I differ from the mainstream. There is a careful balance of responsibility to watchability. I think Fincher, Sorkin, and co. realized that and they took a big risk. I consider it to be an outside-the-box approach to capturing the truth (an extreme case being something like Hayne's I'm Not There). I don't mean this as an insult to Zuckerberg for not participating, but then it is up to the press for the film as well as Zuckerberg's people to mention the artistic merits of the film being placed over the truth... which, yeah kind of sucks but film is a form of free speech yada yada yada.
When it comes to dramatizing true stories/events, it is a very comprehensive puzzle of "you can do this if A is the case but you can't do that if B is the case, but if C is also the case along with B then you can do . . . ". It's like when is it more appropriate to call or text someone with your cell phone? There are a wide variety of exceptions to the "rules."
To continue using recent popular films as an example, I think Affleck's The Town does a great job of explaining to its audience the dramatized facts (Charlestown has a lot of crime) but at the end it is sure to be respectful (saying during the credits that the citizens of Charlestown are not meant to all be depicted in a certain light).