That isn’t the rule either, I guess parent made their point. The first person who stops goes next, right away only matters if their is ambiguity in who stopped first.
I’ve never seen a four way stop in a region that had traffic on the right can always go regardless of stop time. But I’ve only seen four way stops in a few countries.
This is not correct. There are clear instructions on how a 4-way stop should operate and its yielding to the right, if opposite cars are both moving forward, both can go, otherwise the car who has initiative has the right of way. Every driver must come to a complete stop.