Brown is very selective about whom they choose to interview--but, if you make it to interview day, you have an extremely high chance of being accepted. They accept something like 250 out of 300 people they interview each year. Your personal statement, AMCAS application and letters of recommendation REALLY COUNT here (much more so than top grades and MCAT scores).
It seems like you will have the best chance of being picked to be interviewed if you are a non-traditional student who has accomplished interesting things in both the medical and the non-medical realms. At my interview day, we had a stand-up comic who was also an EMT, an HIV researcher who is also a professional dancer, etc. So my advice would be to play up what makes you special outside of the health sector. If you can tie it to why you'd make a good physician, you will have a great shot at Brown.