The FAA is notorious for their draconian ways which has become the impetus behind why air travel is now the safest mode of transportation today. In fact, there hasn't been a hull loss on US soil since 2009, a magnificent safety record.
The FAA is a very hands-on agency. There is an inherent difference to how planes are maintained that touch US soil vs. those in other parts of the world. For example, many planes that fly in South America would never pass FAA inspection and would never be considered airworthy. That means a flight itinerary of LAX-SCL vs. LAX-PTY-SCL are very different when it comes to safety since the plane that departs from Panama is not inspected by the FAA.
So not only is the FAA risking an insurmountable amount of fallout for making this statement, they also have the credibility and processes to stand behind it. With that said, I think it makes prudent sense for other countries to ground their 737 MAX planes since they simply don't have the FAA.