All of these are things that add to their credentials.
You're assuming that professors decide admissions based on a process akin to drunk pin the tail on the donkey.
None of the "luck" you're claiming is somehow unique to the law admissions process. Demonstrating that normal statistical fluctuations apply to HYS hardly invalidates their entire selection process.
(1) Yes, all of these things add to their credentials
(2) Professors always have their own intellectual beliefs. It shouldn't be surprising or at all controversial that they will, at times, exhibit preferences for people who share them.
(3) I'm not trying to "invalidate" a selection process.
I'm merely saying that the notion of something being "HYS material" is just conjured from people making up concepts, trying to feel good about themselves. If you really walk through the streets of Morningside Heights and, as you walk by the Columbia Law student, that you're "more HYS material than he will ever be," there's something wrong.
Yes, on average, the numbers are higher. On average, HYS classes tend to have more accomplishments. But there is nothing in the concept of being "HYS material" other than what you load into it, and I get the sick feeling that some people are just making up this concept to feel like they're special or something. Yes, you're special. No, you're not special because you belong to some arbitrary little club. Yes, you're special because of the qualities you have.