I am from a state school in the midwest with average reputation. Steps 240s/250s/pass, Honors in all rotations m3 expect peds (first rotation), honors in early M4 courses (but hadn't taken peds subI when transcript sent out). Great PS (i think), average LORs (I think), no research, average extracurriculars (few, but really involved in those few). I was senior AOA and University Honors. I did an away rotation at an Ivy league school, and did not feel my experience there was any different than it was at my home institution (maybe even less teaching at the Ivy).
I was offered an interview at every place I applied, including "top" programs like BCRP, CHOP, Stanford, Washington, Hopkins, Northwestern, WashU. I ranked 11 programs, and went on about 18 interviews (I had not spent much time outside of my midwest state and wanted to check a lot of places out).
I matched at #3 on my rank list, but am not a very good interviewer. All things considered, I do not think that being from a state school hurt my application very much.
I hope this scenario helps ease concerns. I absolutely don't think you need to be AOA to have similar success, and I include all of my stats/extracurricular just to help people gage their own competitiveness. I applied to 30 schools b/c i figured that schools like BCRP and Hopkins would not interview my midwest-state school attending resume. Turned out to be a huge waste of money.