> US origins of the key technology here give the US a veto here regardless of ASML's Dutch headquarters.

Is this an actual thing? Genuinely asking. Not that rules and laws seem to matter anymore to the current US administration anyway

Yes, the mechanism is effectively EAR/FDPR and you can check (https://en.wikipedia.org/wiki/Extreme_ultraviolet_lithograph...) for more detailed history, but the EUV technology ASML further developed and commercialized (no small feat) was licensed from a US Govt created consortium by which the government maintains their IP rights.