Which committees screen, though?
In summary, it doesn't look like any school actually has a hard screen with the possible exception of Brown (based on stats). However, most schools (except perhaps Dartmouth and Columbia) require an interview with the health professions advising to determine the suitability of the candidate. I would imagine if there is a glaring problem with the applicant's application (ie no clinical experience, 2.8 GPA, etc), they would be discouraged from applying but not outright stopped. Again, I only attend one of these schools and can only comment with absolute certainty about that particular one, but this is what I have found in my search.
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Harvard: Does not appear to screen, but works with applicant throughout the process via personal advisor to ensure they are competitive (
The Application Process - Faculty of Arts & Sciences)
Yale: Has a required interview where an advisor will discuss whether or not you're a competitive applicant, but not a true screen (
http://ocs.yale.edu/content/health-professions-evaluation-interview)
Princeton: Not officially, but there is an advising letter process which requires an interview, though they state that there are no MCAT or GPA cutoffs to make an applicant eligible for a letter (
http://www.princeton.edu/hpa/applicants/composite-letter/)
Columbia: Appears that the committee letter be written upon student request as long as the student has completed all necessary requirements (such as taking the MCAT) (
https://www.cc-seas.columbia.edu/preprofessional/health/application/recommendations.php)
Dartmouth: Does not have a committee letter. Has a "composite letter" instead with no centralized committee (
Interfolio Composite Letter Process - Dartmouth College)
Penn: Not explicitly, but there is a lengthy process that the applicant goes through prior to getting the committee letter, so I assume if the applicant is too weak, they discourage them from applying - certain questions have to be addressed if GPA is below 3.1 (
http://www.vpul.upenn.edu/careerservices/files/Applicant_Manual_Final.pdf)
Brown: Must have competitive stats (3.6/32 for MD and 3.4/27 for DP) and ECs as well has having taken most of the premed courses (
https://www.brown.edu/academics/college/advising/health-careers/applicants/process#eligibility)
Cornell: Has an "evaluation committee" that adds a letter to the applicant's file as to how suitable they are for the medical profession, but does not seem to actually screen (
http://www.career.cornell.edu/paths/health/medschool/hcec/index.cfm)