You may want to read 'Thermal Physics' by Kittel and Kromer. It is the BIBLE of statistical mechanics and should straighten you out on why a statistical law is just as good as all others. And yes, it goes into great detail about when and how the statistical laws 'emerge', so to speak. Physicists have been 'worried' about what you mention in you comment for about a century and the science is very mature these days. Used copies start at ~$25.

https://www.amazon.com/Thermal-Physics-2nd-Charles-Kittel/dp...