@ucbalumnus has it right.
MCAT and GPA are just the first screener for med school that prevents an applicant getting dropped from consideration.
Name of the graduating institution carries little importance for med school admission. (See p. 14 of Using MCAT Data in 2024 Medical Student Selection which is a survey of med school admission officers about the importance of variety of factors in making admission decisions.)
Medical school admissions are holistic in that once the basic academic metrics are satisfied, other considerations are given very significant weight.
As for “elite” med schools–all US medical school should be considered elite because most applicants (>60%) get zero acceptances. Of those that do get an acceptance only, 33% get more than 1.
Med school rank does not influence job opportunties–unlike law school. All physicians are virtually guaranteed full time employment upon completion of residency training.