I think it will depend on the school. For the most part, I agree with you. Clearly stats are extremely important. But once you reach the stats range for a particular school how do schools decide who to interview? If Duke is looking for students in the 35-37 mcat range and 3.7-3.8 GPA, how many students will fall in that range? Probably thousands but they only interview ~500. At some point, other criteria has to be used in order to narrow the pool of applicants. Depending on the school, recs/EC/secondaries will be weighed differently.
Obv none of us actually knows what goes on during the pre-interview stages. The only personal experience I have involves interviews. While I had some blind interviews, for the most part my interviewers knew my application backwards and forward. As I have elaborated in a previous post, I had an interviewer totally destroy my PS during the interview, resulting in my only waitlist. At another school (my top choice), I spent a lot of time on my secondaries. I tried to make them humorious and interesting. My interviewer loved me before I walked in. His exact words were something like "I really feel like I know you from your secondaries. I don't always get that feeling but yours really stood out." And then during the interview it was relaxed and we had a great convo. It was one of my best interviews.
So to summarize, none of us knows how much of a role secondaries will play. Personally, I put a lot of effort into mine and I think it made a difference. I don't know if it helped me get an interview but I def think it effected my acceptances and actual interviews. How many hours did you spent studying for the mcat? How hard did you work in UG to keep a high GPA? How much time did you devot to research, volunteering, and other EC? Secondaries are really the last hurdle before interviews. If it was me, I would put my best foot forward. I wouldn't want to hurt my chances in anyway when I am this close.