6 hour cooling contradicts 2/4 hour food use rule
The reference that was posted is from an Australian agency, so there is your explanation - you are comparing different standards. 

There is not some natural border between "safe" and "unsafe" foods. You can see "safe" as more of a certificate, like the CE certificates for electronics - it means that a regulation body has defined conditions under which the food is considered "good enough" for eating. What is "good enough" depends on their risk aversion, the mathematical model they use for bacterial growth, the history of food poisoning outbreaks in their country, and many other factors. 

So it is perfectly normal to end up with different food safety rules around the world. Food which has been cooled by that rule will be safe by Australian standards and unsafe by FDA standards. 

If you work at a food business, you have to follow the standards of your own country. If you are a home cook, you can choose for yourself which ones to follow, if any.