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.
That indeed does not exist, but if you do well on these, you are probably pretty eligible for their part-time MS program.