I applied to 9 programs, and so far got rejected from 6. When the rejections were coming in, my only offer was from a "backup school" and I had lost hope that any of my preferred schools would be interested in me. However, I ended up receiving an offer to one of my top choices, which apparently only extended offers to 20 out of over 300 applicants. I still haven't heard from the third school, but I am not holding my breath.
My credentials are certainly not as good as yours: 3.6 GPA (my last 2 years was 3.8); no publishable research, although I had a variety of research and teaching experience; and 1320 GRE (Q: 750, V: 570, A: 3.5). I believe it ultimately came down to research fit and my POI's desire to have my skills in his lab. In my personal statement, I really sold the fact that I had a major interest in software and programming; I found out that my POI's lab is currently undertaking several projects that would benefit from having an in-house programmer. This was definitely a boon when coupled with our compatible research interests.
Like others have said, most likely you were overlooked because of your GRE score. If not, maybe your statement did not express your research goals clearly, or it really came down to your goals not being compatible with the programs/POIs you applied to.