And I was honest: "You know, I don't know which story is the right one."
But I do know this: last time I applied to six universities, only one of which was in the top-20, and I got five rejections and one wait-list (and that for a different program than the one for which I had originally applied). This time I applied to nine schools, seven of which were in the top-20, and I got six offers, two (extended) wait-list offers, and only one definitive rejection.
Obviously, who you know and where you've studied matters. But so does a writing sample of an appropriate length and quality. I'd like to think my successes this time were due to a blend of both, hopefully more of the latter than the former. In the end though, the most important thing is that the system was flexible enough to give me a chance, because, as it turns out, that was all I needed.