This factor cannot be overstated. At top 5 schools fit matters. Now, that doesn't mean that you should try to echo the interests of faculty members at MIT or Stanford or whatever. Rather, it is very important that you know what your interests are and find faculty and schools to match that. Not only can faculty members sniff out BS in your app, but also you'll be much happier researching something that actually interests you.
For example, I consider myself a top-tier caliber applicant, so I applied to three top 5 schools (UIUC, Stanford, JHU; I'm 2 for 3 and waiting for Stanford). Now when I spoke to faculty members, they did mention in passing "great GPA/GRE" but what they really wanted to talk about was their research and how it would interest me (they were right). I did not even bother applying to MIT and Berkeley because they weren't strong in my areas, thus (a) I would be rejected and ( even if accepted, I would be miserable working on their projects.
In short, that MIT reject really bothered me. No one is entitled to admission to a top school regardless of great stats.