I am under the strong impression that most medical schools in the US require green card (legal residency) or citizenship as from examples below
NYU
http://school.med.nyu.edu/md-admissions/how-apply/admissions-requirements-selection-criteria
International Applicants
In view of the large number of applications to the School and the difficulties involved in the application procedure for students abroad, foreign candidates are not encouraged to apply if they are not permanent residents of the United States
YALE
http://admissions.yale.edu/applying-yale-international-student
Special Note to International Students Intending to Study Medicine
It is extremely difficult for international applicants who are not citizens or permanent residents of the United States to gain admission to U.S. medical schools. State-supported medical schools rarely consider international applicants for admission, and those private schools that do accept applications generally require that international students place in escrow an amount ranging from one to four years’ tuition and fees (USD 40,000–200,000). There are very few scholarships available for medical schools in the U.S., and to qualify for U.S. government-sponsored loans, the applicant must be a citizen or permanent resident. International applicants who are considering a career as a medical doctor and hope to receive their education at an American medical school should think carefully before applying for admission to an undergraduate program in the United States.
However, Harvard does report some success from link below
http://www.ocs.fas.harvard.edu/students/careers/medicine/international.htm