Exactly this. The reasonable thing to do would've been to differentiate refugees from others and proceed to help the refugees because there's no question about that.
Edit: Wait, I take it by the downvotes that you think people should not be screened and that everyone who shows up at the borders is a distressed refugee fleeing war? I am a Third World citizen and I know for a fact that no one thinks of Europe as a dreamland so yeah, you're good, refugees are all you've been/will be getting. /s