Any problems here?

That people are stupefyingly irrational about risks, especially in regards to medicine.

As an example; my paternal grandmother died of a treatable cancer less than a year before I was born, out of a fear of doctors which she had picked up from post-war propaganda about the T4 euthenasia program. Now this is a woman who was otherwise as healthy as they come, living in America decades after the fact, refusing to go in for treatment because she was worried some oncologist was going to declare a full-blooded German immigrant as genetically impure and kill her to improve the Aryan race.

Now granted that's a rather extreme case, and she wasn't exactly stable on a good day from what I hear, but the point is that whatever bits of crazy we have get amplified completely out of proportion when medicine comes into it. People already get scared out of seeking treatment over rumors of mythical death panels or autism-causing vaccine programs, so you can only imagine how nutty they would get over even a small risk of actual government-sanctioned murder in hospitals.

(Not to mention that there are quite a lot of people with a perfectly legitimate reason to believe those RNGs might "just happen" to come up in their cases if they went in for treatment; it's not like American bureaucrats have never abused their power to target political enemies before.)