While in a de jure sense this is true, de facto the FAA effectively does have oversight over many (maybe most) commercial aircraft all over the world. Small countries in particular do not have the resources necessary to exercise meaningful oversight over every type of aircraft on the planet, and defer to FAA decisions in virtually every respect for Boeing and other American-made aircraft, and the US FAA and NTSB are involved in the investigation of virtually every incident involving a Boeing aircraft anywhere in the world.

Even larger, well-resourced geopolitical entities like the EU rely heavily on the FAA to do its job for Boeing aircraft, much as the FAA relies on the EASA to do its job for Airbus aircraft. It's not pure rubber stamping, but it's close enough that things like this can pretty easily happen if a manufacturer's home agency falls asleep at the switch.

An example of the FAA's influence: Airworthiness regulations are so closely coordinated that special numbering is used by Canada, Europe, and Japan to match the numbering of FAA airworthiness regulations for easy cross-referencing. The FAA is also delegated air traffic control responsibility for much of the world's international airspace by the ICAO.

It is basically impossible to fly a commercial aircraft on Earth without being under the – possibly very heavy – influence of US civil aviation authorities, and it would take a great many resources and serious, concerted political will by many countries to change that.