The truth is there is a larget percentage of freshmen BME who are considering pre-med. But as the years pass by more and more drop the pre-med position. This is for a number of reasons. The of the ones that are pre-med usually drop out of BME entirely and take an "easier" major. Others drop out of pre-med and BME and do something entirely different. And lastly the vast majority of BME who are pre-med drop pre-med and stick with BME because, as my advisor says, people find BME interesting enough that they would rather go to grad school than med school.
Not entirely. They can't stop you from applying or getting a recommendation from your advisor. But if you go against your advisor's suggestion (of not applying), then most likely your recommendation will state that (and look bad), and you won't get in anyways.