Some of my very favorite mystery writers have tons of non-direct stuff -- Louise Penny, for example. I just re-read the opening to Still Life, and she gives you a body and detective on page one, but then she wanders off and deliberately confuses you and introduces you to a ton of other characters who don't even know about the body yet for pages on end. I think Penny gets away with it because the rest of the stuff is so interesting. She's wildly popular, so it's not just my idiosyncratic response.
But it means that when I have critiquers (maybe 4-5 out of 15 so far) who are telling me to cut the flashbacks in the first chapter, I'm not sure if that means I'm not writing them compellingly enough, or if it means they expect something else from a murder mystery, something faster-paced and more action-oriented. If the latter, and if they feel strongly about it, I think this may not be the book for them, because there's going to be an awful lot of people hanging out and talking, I expect.
But I wonder if, assuming the latter is the case, they'd feel the same way about a literary book of mine that had mysteries, but not a murder. Is it the murder that slides it directly into a different genre and mode for them? I'm not sure.
My flashbacks are staying, though, I'm pretty sure. :-)