With all due respect, that is an uninformative study. Of course, the top privates are top feeders to top professional schools – since the top privates select for strong test takers. It should be no surprise that the grads of top privates ace teh LSAT, MCAT, GMAT and GRE.
Not to mention that the big public Unis have a lot of grads who have zero interest in grad/professional school. For example, an EECS grad will have plenty of job opportunities.