I agree a lot with the first half. The second half, less so.
There are many games where the player characters function under one specific set of rules, and the setting simply doesn't. This includes games where the PCs are explicitly the "heroes" of the setting that play by their own rules, like Draw Steel or most superhero games. It includes narrative focused games where rules are based on the story flow and happily sacrifice setting details to achieve other goals. And on the extreme end it includes gonzo games where the setting has ostensibly no rules, like Troika or Human Occupied Landfill.
Even D&D varies a lot with having rules about how the setting functions. On one side you have 3e, where all the monsters have stat blocks that effectively match the details of a PC build. On the other side you have early Arneson style DMing, where the setting rules are ostensibly a black box. And you have 5e somewhere in the middle, where Legendary Actions are there specifically to throw a wrench in the rules the characters play by.
So, yes, the rules definitely determine how the characters interact with the setting. But what, if any, rules the setting plays by is a very different discussion, driven by very different wants and needs.