It also says when (while she was not at work).
My opinion is that really shouldn't matter what you've done, if you weren't on the clock, your employer has nothing to say about it.
I can see exceptions when you are misrepresenting yourself as acting in an official capacity or if you are clearly "the public face" of the company (like an on-air personality or public spokesperson). On the face of it, none of that applies here.
Some people do, about 20% in Saskatchewan.
I've been getting the annual flu vaccine since it became available.
I don't particularly worry about disease and accidents and definitely don't live in fear, but I take standard precautions: vaccinations, diet, fitness, PPE in my shop, etc. It's all relatively simple and mostly low effort.