The contract is with the foreign carrier, but you raise a good point about some of the crew leasing companies being based in the U.S.
The reason for leaving, if it even happened, would be to care for elderly parents that would have no one else to help them. They have always been there for me and I'd hate to be in a position where they needed my help and I was unable to leave. It has nothing to do with greed or jumping ship for a better opportunity.