Oh that would be quite easy for them since all these companies can ship the parts wherever ASML wants. They rely a lot of companies in Germany and Belgium, Korea, Taiwan, Japan, USA too.
On one hand that is true, but I think for some of the critical parts, I guess they do have a rather close relationship with, and having regular meetings with. Having regular meetings with a company that is at two hour drive is a bit easier than at a different continent. And then there are also culture changes that require you to build a relationship with your suppliers.