I mean it's literally beholden to the USA congress and it's most meaningful parts are made in the USA. There is a reason why they fall in line with every USA export control and restriction.
If ASML is Europe's then I'd say all of Europe is the USA's.
But more importantly, ASML does exactly what America tells them to do.
And Europe for the most part does as well.
Sorry, I wish Europe had the fortitude to not be subordinated to the US, but that's how it is.