I've been thinking about this myself, because I'm working on a story that I want to be accurate to historical fact, though the story I'm writing is not something that would ever, could ever have happened. It's walking a line between setting a scene for realism and inserting a fanciful storylines.

I am a stickler for research, I hate it when I come across something that just runs roughshod over fact, despite choosing to place the story in a situation that does have context. I'm a crap researcher. I'll go back and clean up, but when I'm writing I don't have the patience for it. That's why I fudge as much as I can to blur the lines and avoid precise details, but some things you just can't gloss over. My goal is to stay as accurate as I can while leaving room for the possibilities of my storyline.