As has been posted a number of times already, an applicant's writing sample and SOP are weighed most heavily by committees. Grades, institutions attended, GRE scores, etc. are of secondary importance but not negligible. This is because Universities want to know that the applicants they accept (and fund) are those most appropriate and apt to succeed. So yes, there are success stories (that I know of) in which an applicant has been accepted into a higher tier university despite the odds--we should say competition, these are people after all--because they were able to show convincingly that they were a good choice. To be more specific, I know of a student in similar circumstances, that is, one who attended a good but not great university for their BA, had good but not great grades, acceptable GRE scores, and went to a good but not great university to pursue an MA. This person excelled in their MA program, however, and was fortunate enough to publish a paper in a highly competitive peer-reviewed journal. This proved enough to win them entrance into all the Ivy-League schools they applied to, which they turned down to go to a school that seemed a better personal fit--UT Austin, a great school nonetheless. This might seem insane but only in a world in which the pedigree of a school is more important than its ability, if it has one, to foster creativity and personal success as these are the things that matter in life, professional and beyond. Beating the odds seems more to me like achieving the goal of recognition, which is a fair personal goal, but not--in my mind--of the highest priority. What matters more I would argue is finding a school that will allow you (and me) to develop professionally: learn how to teach students and contribute to academic discourse. And fortunately for all of us there are many, many schools like this in the US.