You're wrong, your parent is correct. NL government had to block sales of ASML EUV machines to China on the US's request since they didn't want to enable China build advanced chips.

ASML definitely wanted to sell to China to increase their quarterly revenues but couldn't because the US owns the IP for the EUV tech and ASML's EUV light sources are made by CYMER in the US, which ASML bought but they're still under US trade restrictions.

So no, ASML and the NL government have to dance according to the moves dictated by the US gov as they own the keys to EUV tech, not ASML/NL.

Well, to an extent.

But as we saw with the Evo Morales grounding incident https://en.wikipedia.org/wiki/Evo_Morales_grounding_incident there's still a certain amount of jumping.

ASML has suppliers in the US, so if the US does not like what ASML/NL are doing they could block exports of certain components to certain destinations.

Also remember that a lot (all?) of the circuit design software is US-based, so the supply chain could be squeezed from that direction as well.

Europe is still doing it, and when they don’t the us applies pressure through its closest European Allies. The us is very much still involved in classic Cold War stuff in Europe. The Ukrainian war has been very good to American exports of arms and liquid gas.