This is very much an over-generalization. My PhD advisor is an NAE member and very well known in his field. He had a number of undergraduate students working in his lab while I was a graduate student, nearly all of which he knew well enough to write a pretty fantastic (or damning, as the case may be) letter of reference for applying to other graduate schools. As it turned out, most of them loved his group so much that if they went to graduate school, they stayed with him anyway, but the few that left would have got a very nice letter from a very well-known professor.
Now we have n=1 for both sides of that story. I guess that means it’s 50/50 nationwide, right?