> A million dots scattered randomly over a graph can all land on the exact same coordinate if it’s truly random.

It won't happen though. 0.00000000% chance it happens even once in a trillion attempts.

> What most people intuit as random is some sort of noise function that is generally dispersed and doesn’t trigger the pattern matching part of their brain

Yes, people intuit the texture of random wrong in a situation where most buckets are empty. But when you have orders of magnitude more events than buckets, that effect doesn't apply. You get pretty even results that people expect.