Will anybody actually read your research and teaching statements? When applying to faculty jobs, how much weight is given to your research/teaching statements?  Talking with a few folks on admissions committees at Very Good Departments in Big Research Universities, I was told in no uncertain terms that


your letters get you the interview,
your talk and individual meetings get you the job,
nothing else really matters,


where "nothing" includes your research statement, your teaching statement, the content of your publications, or your hairdo.  Of course, I am working with a very small sample here.  How true is this sentiment?  (And if it is true, why keep asking us young folks to write these hackneyed teaching statements that nobody ever reads?)  More importantly,

Question: For those who have been on faculty hiring committees, what are the actual criteria you use to invite applicants?

By actual (in bold and italics) I don't mean "what the job posting specifies" or "what the department charter says you're supposed do," but rather "how you actually make these decisions in a meeting right before lunch while preoccupied with a grant proposal due at midnight and the fact that the cafeteria is going to fill up with noisy smelly undergrads if you don't get there soon."
I am the chair of the faculty recruiting committee in a Very Good Department at a Big Research University.  I read research and teaching statements.

I need to know that you have a compelling agenda for your future research; your letters won't talk about that at all.  I need to know that you can describe and motivate your research agenda well enough to attract external research funding.  I need to know that you know why (not just "that") your work is interesting, visible, important, and likely to have high impact.  I need to know that you communicate clearly enough to be a good teacher, and that you care enough about teaching to formulate a coherent teaching philosophy.  I need to know that your research, teaching, and career goals—as you describe them—match those of my department.  I need to know that you are taking the recruiting process seriously.

In the long run, your publications (which I also read) and your recommendation letters are probably more important.  But saying that your statements have no importance is a dangerous exaggeration.

Also, I don't eat in the cafeteria.