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.
This is true in every state.
https://www.nhtsa.gov/sites/nhtsa.gov/files/rightofwayrules....
It is correct and is literally the first bullet on the pdf you linked. First to stop is first to go.
Yielding to the right only applies if you stop at roughly the same time, otherwise first to stop goes first. It's the first bullet point in your link.
right of way