What I primarily learned is - GPA matters, and research experience (or good recommendations or amazing SOP or good GRE scores) cannot completely make up for the lack of a good GPA. My GPA was 7.15/10 with from a top undergraduate institution in India (well recognized in the US), which is not very bad but looks horrible if converted to a 4 point scale. I got through all my safe schools (UCI, Minnesota, Stony Brook) and got rejects from all the top schools (UChicago, UIUC, UWM) in my field. I had good research experience (internship in Europe), one first author publication and another paper submitted - both to good journals, strong recommendations from two famous people in my field, and good GRE scores, but that didn't help really.
Another student from my batch had a good GPA (above 8.6/10), no publications (though a submitted paper I suppose), decent recommendations, good GRE scores, and she got through all top schools (Stanford, UCLA etc). I know there cannot be a direct objective comparison between two applications, but from what it looks like, my application probably got 'filtered out' from all top schools because of a low GPA.