We can properly vet. Vetting doesn't mean that everyone is 100% safe. We will always have enemies trying to abuse a refugee system. It's also important to remember that the screening process takes a long time. They will have background checks and multiple interviews while waiting for over a year to try to get into the country. After they are in the country they will still have to pass more screenings if they need to get a green card. The U.S. program is much better than Europe's. People aren't just flooding into our country. I don't know where you got your numbers, but we have already taken in almost 12,000 Syrian refugees and I imagine we would have heard something about it if we had 240-1200 terrorists successfully infiltrating the refugee program. I think the numbers are a lot lower than you're guessing.
Wait. Stop.
I'm not refusing to be honest. You are claiming that there are no records. That is not true. Some refugees may not have records, but don't act like there is no data in the system. Comey has said both that there are gaps and also that the FBI has an effective vetting process. Johnson has expressed concern while also stating the process is constantly improving and they should stay on their current trajectory. I will admit that I am less convinced after reading up on the totality of their comments, but seeing as they overall support the program than I do too.