The only data on Princeton's applicants that I could find online is here:
http://www.princeton.edu/hpa/suggested-reading/12-13-Applicant-Guide-FINAL.pdf. It is a compilation from 2009-2012 so it is a little bit outdated, but the metrics should not have changed that drastically since then.
Some things to note:
-In Table 4 on page 40, the total number of medical applicants was 487 (122 per year on average). This number is in line with the 2013 cycle (124) and the 2015 cycle (116).
-According to elfe's "The Most Premedical Universities" thread, in that given year, Harvard had 323 applicants, Yale had 232, and Stanford had 283. However, in that same data set, Princeton is listed with 171 which is most definitely too high. Unfortunately the link to that year's AAMC Table A-2 where he extracted the data is broken so it's hard to resolve this discrepancy.
-The current cycle's "Undergraduate Institutions Supplying 100 or More White Applicants" (
https://www.aamc.org/download/321458/data/factstablea2-7.pdf) has Harvard with 122 and Yale with 124. Princeton didn't make the cut. For Asian applicants (
https://www.aamc.org/download/321456/data/factstablea2-6.pdf), Harvard had 91, Yale had 87, and Princeton had 62.
-For 2009-2012, according to page 39, there were only 18 MD/PhD matriculants. Putting this together with Lucca's quoted post implies that Princeton is not only supplying fewer MD applicants overall, but even fewer MD/PhD applicants proportionally compared to Harvard and Yale.
As kringle previously mentioned, the reduced number of applicants may be attributed to grade deflation, the lack of an affiliated medical school, and/or the strong banking and consulting culture. Princeton has ~5390 undergrads whereas Yale has ~5450, so an objectively lower percentage of students are choosing to pursue medical school. However, if you examine the acceptance matrix on page 41, 90% of applicants got in which isn't bad. If you include those who did science post-graduate work, the acceptance rate dropped to 88% (429/487). The fact that 12.3% of applicants had 39+ and 40.5% had 36+ MCAT may reflect rigorous grading. The committee does not appear to screen as indicated by the "low" GPA/MCAT outliers, but this does not rule out self-selection which may be significant for both prospective MD and MD/PhD applicants.
I do believe that Harvard and Yale are better for aspiring pre-meds. Regardless, "Between 35% and 40% of [Princeton] students who matriculated to medical school in the past four years is
attending a top 10 US News & World Report research school." so it's still a solid undergraduate university for those that dream big.