No, they're a private business although they do have government contracts. I've heard they've threatened to fire employees over talking about joining a union before but I have my doubts about that. I am a non-exempt employee, whatever that means.
The conversation was with the facility's HR manager. She said they wanted me to be evaluated by a psychologist, and that they'll find one despite me having a psychiatrist of my own. She also said that once I'm cleared through the psychologist and EAP I'll be allowed to return to work. She used the phrase "return to work". This is part of why I record my calls, largely for my own reference. It's actually an app on my phone. It automatically records them all.
Since they wont tell me what she said I don't know for certain but my friends who still work there tell me she said I claimed something, and it's a bit grotesque and offensive so be warned, "smelled like a freshly ****ed five year old". The time she claims I said that was almost a full 24 hour before she reported her claim. It was near some incredibally loud machinery which obstructs anyone hearing anything that isn't yelled at them from more than 10 feet away. We're also required to wear ear plugs while on the floor. No one was around when her claim would have occurred either. It's her word against mine. As I stated earlier, she had also been a temp for all of three days at that point.
I use an app on my phone that automatically records all of my calls. No external devices are being connected. I'm not sure if that helps or not.

