Literally nobody is saying that.
You do realize that this is the case with basically every decision a politician makes? Are you really this naive about how the world works? Or are you too old to remember life's complexities...
So, you have shifted the goal posts. It was originally "we have no legal obligation." Now, it's "okay, maybe we have some legal obligation, but that legal obligation doesn't specify the exact number of people." Actually, that's generous. You shifted even further by adding "despite material security risks." No. This just isn't how it works.
First, you are correct. We do have some ability to pick and choose. Nobody has suggested or argued otherwise. In fact, several people have mentioned that we pick and choose, explaining numerous times that the bar for refugee status is extremely high. This is our picking and choosing. Much of this is codified. It's not just the whim of some government dudes. Second, if you are looking for the defined obligation to take X number of people, you should look to Section 207 of the INA, which provides the mechanisms for determining that number. There is tons of info out there about how that number is reached. Here is some of it:
I also would suggest reading the Congressional Record, if you would like more information about how we determine X number. This number is set every year by Congress and the president.
Changing policy to reduce the number of refugees admitted and to increase the stringency of screening process are totally reasonable suggestions to address the concerns you are raising. I haven't said your concerns are invalid. I've said you don't understand the proper way to address your concerns. These policy discussions can't exist when people in the conversation don't understand some of the basic legal frameworks under which U.S. refugee policy is operating. At some point, it's not productive to continue the conversation, if you are not interested in understanding that framework.