You know, reading the link you gave, it’s plain that DHS is refusing to vaccinate. But their reason and logic shouldn’t prevent outside sources of vaccination. I don’t see them budging, but by washing their hands of vaccination, they open a door to 3rd parties handling “the complexities of operating vaccination programs.”
That’s predicated on them giving a shit. Still, if I were them and there were a way to polish my image on someone else’s dime, I’d find a way.