I haven't applied yet (will do this cycle), but a friend of mine might fall under this category. She applied during this past cycle, has a 3.62 from UCLA (with a strong upward trend) and a 30 (12 BS, 10 PS, 8 VR), and has the basic extra curriculars (research for a summer w/ no pubs, hospital volunteering, tutoring) but nothing THAT special. She is NOT a URM (caucasian). However, her essay was very touching and her LOR's supposedly very good.
She got into Georgetown, UChicago, Creighton, Temple, and a few others, and was most likely headed to Georgetown until she got interviews from UCLA and UCSF out of nowhere pretty late in the cycle (Feb and March, respectively). Last week she got into UCSF. The #4 Ranked school for Research by US News! Look at their averages! She was as shocked as anyone.
People on this site would talk smack about a 30, but hey, look where it got her!