I will say that even though there may be no legal action available here, I think the student has a right to inquire about the evidence they have that he made racist and insensitive comments. Let's say that these accusations were false or doctored, but the student never inquired -- that could have been problematic as well because the student wouldn't have had any recourse in a situation they were not at fault for. If the school comes to the conclusion after an investigation that the alleged statements are true, then they have a right to rescind a provisional acceptance. Once you matriculate, you and the school you attend enter into a mutually beneficial (or detrimental) relationship. The school doesn't do well, it casts doubt on the student body. The student body does something awful, it reflects badly on the school. I think the school has a right, prior to admission, to deny an applicant if they decide that that applicant doesn't fit what they want for their entering class (professionalism included) and may cause harm to their reputation upon entrance. That is not to say that that is what would have happened had this particular student matriculated, but just a thought.
I would also agree with some that the use of e-mail a day prior to a major holiday (where you will be celebrating with family and where the medical school office will be closed) was not the best way to go about things. I think the best course of action would have been to e-mail on that following Monday, with contact information for someone he could speak to about the situation if he felt inclined to do so. Or a phone call would have worked as well.
Either way, I think the individual in question meant to stick up for a group he felt was being attacked, but didn't handle it in the best way. I really do hope that things work out for the best.