The one flaw in your reasoning is that Mary worked as a cook in people's homes. No middlemen like a restaurant. Also, she didn't know she was infected, and even after being quarantined and informed that she was, continued to uphold that she was not, putting the responsibility not on the bacteria, but her.
It's not a flaw in reasoning, it's a misunderstanding of the situation at hand, but the reasoning still is the same. It's the responsibility of the people hiring her to ask her if she has tested positive for this disease, or to check references to see if prior employes are sick, etc. If she deliberately misrepresents this, saying she was never told she had the disease or saying she didn't have prior employers (which is different from saying she doesn't want to provide references), then she would again be acting fraudulently. In a lot of anarchist societies, this would get you a trade ban which is effectively death by starvation.
Possibly some charitable group would offer to feed her if she agreed to quarantine herself.