I think the bold part is the problem. They may have honest intentions, but there is no way to know if they are just shunning work or not.
I don't know if you mean a drug-based treatment for anxiety, and I can understand people being sceptical about medication. But perhaps they could be referred to a psychologist for therapy? Quite apart from that, I think many of us will need that once we get back to things. So I understand the anxiety, but we cannot stay home forever.
Anyway, tough choice. Do you have the option to refer them to a psychologist for an evaluation of their anxiety? If the moral dilemma hinges on whether they have anxiety or not, a psychologist could be a better judge of that. And perhaps they'd have some tools to persuade them to come to therapy as well?