Well....

The reason he/she couldn't get into medical school is because he/she is not a top student at P.  If he/she is not a top student at P then he/she is unlikely to be a top student at a good state university.  You have to be the top student at top school to be able to take advantage of top schoos' benefit.  If he/she attended P and can't get into good medical school then he/she will has a even slimer chance to get to top medical school if he/she graduated from a state school.  GPA will not be much different regardless he/she is at P or a state school though P has a stronger pool of students.  Thoguh people complain about GPA deflation at P but it's exaggerated and medical school admission officers have unusual ability to evaluate GPA from different schools.  One reason people have an impression that P's GPA is deflated is also due to composition of different majors.  We know GPA is always low for sciences, engineering and other hard science majors but relatively higher for humanities.  We know P has more science but fewer humanity students.  To comprare science students' GPA in H, Y, P, MIT and other top state schools, I doubt there are much dufferences.  Though there are probably some small differences but this small differences will be taken into account by admission officers.  We work at a top medical school of a not very wellknown university, one of the resident told us the interviewing professor blantly told him the reason he got the interview is because he graduated from Smith.  You can image how many students didn't even have the chance to get an interview. 

So top school does help and help a lot sometimes.  But you have to be a good student in top school.  We also know a Harvard graduate who had a hard time getting even into second-tier medical school due to low GPA.  Will he/she get a better GPA at state school?  I doubt.  Since we know he/she is over-positioned to Harvard.  He/she doesn't derserve to be at Harvard.  But we all know many Harvard students don't deserve to be there.  Also some good students in state school do deserve to be at Harvard.