Re: Public Humiliation As a Punishment
yes, they can do that. If you don't want to do it, you can accept whatever other penalty they choose. I'm thinking firing would be high on the list of alternative punishments.
as to anybody with medical issues: if they qualify for accommodation under the ADA they could be excused from the demand. Of course it is likely that other alternative punishment might be offered.
I am not an attorney and any advice is not to be construed as legal advice. You might even want to ignore my advice. Actually, there are plenty of real attorneys that you might want to ignore as well.