"Vetting" nice bureaucrat word, not defined in dictionaries. The word appears in my Webster's but the definition concerns veterinary care for animals. We think the bureaucrats mean checking a refugee's background with his home country authorities. You ask questions like "is this person really a citizen of your country?" and "can we see his police records?" and "Was he gainfully employed before he left your country for America?" and "Did he have a driver's license?" and "What are the names of his wife and children?" and "How far did he go in schooling?"
For real countries, for example England or Japan, this works. There are authorities over there, we know who they are, they have access to written records and they want to cooperate with the United States because of the 800 pound gorilla effect. (What do you say to an 800 pound gorilla? Ans: Sir!) We can believe what the authorities of real countries tell us.
This doesn't work for Syria and similar places. In Syria the authorities are either the Bashar Assad regime or the various rebel groups. Depends on where you telephone. We cannot believe anything that either group will tell us. The records may well have been bombed or shelled or burned.
So no matter what anyone says, admitting a refugee from places like Syria is a risk, they might be enemy agents looking to do us harm. We cannot get trustworthy information from their home authorities, mostly because there aren't any left. The best we can do is interview them, using sympathetic interviewers who speak their mother tongue, and know the area from which the refugee claims he is coming from. I'd say a good interviewer could catch many, but not all, enemy agents pretending to be refugees.
The refugees have suffered terribly, you don't flee your homeland unless things get really bad. I feel sorry for them and want to help them out. Letting them into the United States is a great big help out. And, we need young working age immigrants to keep our population growing.
And, I don't worry about enemy agents infiltrating as refugees. Was I ISIS or the like, and I wanted to get an agent into the US, I'd come up with papers and plane fare to Canada. Then he could walk across the border just about anywhere. More dependable than being a refugee who might or might not get admitted.