There is randomness, but there is far less randomness than appears by looking at the acceptance rate. For example, we know that the admit rate of recruited athletes at Harvard is about 83% based upon data released from the SFFA lawsuit. Essentially, Harvard was a safety for them.
Likewise there are certain academic competitions that are themselves close to a golden ticket for the winners. One that I followed closely resulted in an average of 3 HYPSM acceptances per winner. For these applicants, the HYPSM were effectively low match schools. There is a different award where I am seeing that roughly 80% get into at least one HYPSM based upon a sample set of dozens, making each HYPSM a high match school. In practice, the HYPSMs are not “reaches for everyone”.
Given the fact that some categories of students have much higher acceptance rates, then the flip side is that for most other unhooked kids, the acceptance rate approaches zero. There are certainly borderline cases who don’t get accepted, but if these students planned their range of apps properly and paid attention to them, they will typically get accepted a notch below, hence the rejected at Stanford but accepted at Vanderbilt scenario.
ETA: There is an old but still active thread that lists the prestigious awards which are ranked 1-10, where 10 = Recruited Athlete (closest to a sure thing). A lot of people dismiss this list, but I have nearly current information on the outcomes of students that won at least one of four awards, one at level 9, two at level 8, and one at level 7. For each award I am talking dozens of students, a small number of which have multiple awards. Here is what I saw in terms of outcomes:
Level 9: Average of 3 HYPSM acceptances
Level 8: 80% accepted to at least one HYPSM
Level 7: 35% accepted to at least one HYPSM
I cannot speak to the accuracy of the remaining awards and how they are listed, but there seems to be a lot of collective wisdom in this list: