Yep, that's how I see it.
In the interests of full disclosure, I have family who are descended from people who were rejected at the American border. Some went to Mexico. Others went back to Europe and yeah, some were killed there.
Vetting does not have to be perfect (it won't be. Anyone looking for a 100% safe process should also be searching for unicorns). Yes, a mistake might be made. And it's possible that it will be a horrible one. The only guarantee here is that shutting our borders or opening them will be an error, one way or the other. Opening our borders will, I believe, be less of an error.