All the comments demonstrate a belief that this is some right-wing anti-vaxxer, which seems like a stretch, given that they sought healthcare in the first place.
What if divulging their personal information leads to them being reported by ICE?
I think that's a dangerous deflection of blame away from the power structures and people within them that manifested and fostered this reality. The answer to institutional nihilism reaching actively harmful levels is not to antagonize the common man, and part of the reason why is such antagonism is one of the many ways you build such a culture in the first place.
No, this is a true-to-life scale example of the Constitution’s reservation to the States to regulate the health, welfare, and moral qualities of their populace.
No. Because information gained by torture isn’t likely to be accurate. At some point, they will say whatever you want them to say. The plea system has enough bad outcomes due to corrupt prosecutors and police.
Torture isn't the answer, but if antivax wants to have its moment then it is time to counter that by getting more serious about control of or punishment for people who are voluntarily spreading contagious disease. Of course the places that will suffer the most will be least likely to enforce anything along those lines, so the world will likely continue to get dumber without relief.
What if divulging their personal information leads to them being reported by ICE?
There's lives at stake, possibly a large number. The suspect definitely has the information needed to reduce suffering and death.