Being a graduate of Brown PLME and now interviewing students for admission, I know one of the important characteristic is having ability to succeed in an academically challenging and stimulating environment. Being able to take advantage of what Brown has to offer and utilize the resource to change the world for the better is next on the list. If these are satisfied, then admission to Brown is strongly considered.
Once the student has been admitted to Brown, then the application is reviewed by PLME admission reviewers. The PLME does not spend time reviewing application of someone who does not even gain admission to Brown in the first place. So the application has to be compatible with both Brown undergraduate as well as med school.
For PLME consideration, interest/reason for medicine becomes important. I agree that PLME is not looking for candidates who is only focused on medicine and not Brown. For those who cares about the reputation/ranking of HYPMS, the real focus of Brown PLME education is lost on them. The program is about opening up opportunity to pursue passion in and outside of medical fields, not merely to achieve stamp of approval by ranking. By taking the pressure off college performance and medical school applications, the PLME student can try something outside of their comfort zone as well as diving in deep to pursue their interests without fear of appearing not-medical school compatible.
PLME candidates are discouraged to use Brown medical school as safety, and would have to give up medical school spot to regular applicants if student decides to apply out. The most successful PLME student is someone who is able to utilize the academic and extracurricular freedom to pursue their passion without worrying about medical school application process.
As for whether SAT of 2200 is sufficient, I would say that score is compatible with academic success at Brown, or HYPMS, no significantly different than getting 2350. So my advice is focusing on articulating how you would benefit from an environment like Brown, and how others at Brown can benefit from having you in its community.
(Disclosure-personal opinion above, not official Brown statement. I am a graduate of Brown PLME, Harvard Public Health, and faculty at Stanford Medical School.)