If HR says that they’re lying. It isn’t true.
Um... no it isn't. Most states are right to work. No, you don't need to give severance. No, you don't need to announce it. And yes, that's all perfectly legal.
Is there a theoretical risk that an employee can try to sue you and burn a bunch of your money? Yes, but that risk always exists. Someone could try to sue you always, doesn't mean they'll win.
In actuality the risk is so incredibly small it's not worth thinking about.