@otisp . . .
Sorry for my misinterpretation of your quote in bold. I did think that that (that, that that) was perhaps what you meant, but since OP was seeking advice for undergrad, I thought you were alluding to both universities having similar qualifications for undergrad entry, and this reflected in their having similar acceptance rates to med school, even if the order was reversed. Your statement is attached though, so it does flow better with how you just re-presented it or clarified it.
A private university (Pomona, SCU or Stanford) does have a natural advantage in that its student body will have a greater chance to be accepted to public SOMs in their native states, and some within its students will have the funding to attend without regard to cost at private SOMs. A lot of UCLA grads hope for a UC SOM admission, but because of the competition, most will be attending out of state. In other words, their rate ~ 50% is good, even when compared to Pomona’s ~ 80% because of the previously mentioned inherent advantages of privates, along with the shear number of UCLA applicants.
And It should be a brand new day for the UCLA basketball team: they’ll be hard-nosed and defensively minded. It should be fun.
Edit: I might provide support for my estimations of UCLA’s stats. Some of us are on a crusade for the colleges to provide uniform CDS stats which will benefit the applicant; I’d like to see Pomona present unweighted gpa information instead of just ignoring it.