My understanding is that they can "process" it outside, but the "Data Controller" should be a European legal entity. After all, they are not saying "we are moving everyone data to US", they say "we are moving UK customers to US". I don't doubt they can do it, but I'm not a UK customer, that's the point.

Incorrect. It is legal to process data outside the EU. They have to be compliant with GDPR. GDPR does not require the data to processed within the EU borders.