Ukrainian refugees are high-quality and won’t require arm-twisting to take. I would expect countries to fight over who gets them.
When you accept refugees you’re also accepting the pain of side effects from accepting those refugees. Refugees from some places come with fewer side effects depending on compatibility with the host country and skills and education of the refugees.
your elaboration is accurate and fine.
I think they were just speaking very abruptly. But a different phrase would be better.