[WhitneyLand]

I can't see any reason to believe this is true. It's not stated or even alluded to in their literature or admissions criteria.

Moreover even if it increases your chances a bit, it's a massive investment with no guarantee. Why not simply let the students who demonstrate excellence in earning the certificate a chance to spend another 50k for a degree?

The reason is to maintain artificial scarcity. Stanford has done a lot of great things and all the grads I've worked with have been top notch. However in some ways, Stanford is to education as De Beers is to diamonds.