The tweet, or even any public response from DHS is stupid. Just stupid PR.
But I can follow why doctors might get turned away. Someone shows up with needles and vials that you don’t know asking for physical contact with detainees, you don’t just let them in. Chances are they are good people with good intentions, but how do you confirm? So obviously there should be a way of credentialing volunteers. Local schools manage it. DHS should be no less capable.
Unfortunately, whoever gives the thumbs up will be overly cautious. One sensitivity for the credentialing might be separating people who are there purely to help vs those that will use the access for PR or politics. So it might seem less risky to turn everyone away and take the heat than allow access and end up on TV the next day.