Yes it was developed by the US.
ASML also created the deals with Zeiss and other European companies which were critical in getting all the necessary components created to make EUV happen. None of this would have happened with Jos Benschop and Fred Bijkerk (in the Netherlands).
I agree that some research was done in Japan, Russia, and the US, but this is the case for basically every technology, it's never the case that only one country is responsible solely for something. I'm pointing out (correctly), that ASML kicked ass with EUV tech in a way that no other company did, including Intel, which shows they have something that no other company has. Again, if it was so easy, why isn't an American company making those machines which are critical for the entire worlds security and productivity?
If the tech was so easy and America held all the cards, the machines would be made in America, end of story.