people get into reach schools every year.

From a perspective of a medical resident in a competitive field, every inch of academic cred helps. Kids who went to big name schools had an edge up on the other applicants to medical schools and residencies. Stanford would help him much, much more with medical school placement than BYU, in about the same magnitude that BYU would place him better than UVU. For example, a 37 on the MCAT out of BYU with ~4.0 will get an interview at Yale. A 37 MCAT and a ~4.0 out of Stanford gets you into Yale and probably Harvard or Hopkins.

The Stanford name would then follow him forever, probably giving him an edge for years and years to come.

That's the academic and career argument.

I would be awfully tempted to send my kid to Stanford, but it would depend on his strengths and abilities. But for now, sounds like your nephew just needs to keep up the good work and not be disappointed if it doesn't work out. Then there's the whole meeting a wife thing.