I guess the question is whether they meet the diagnostic criteria you use for clinical anxiety. Whether or not they want to be treated shouldn't determine whether they have the condition. How likely is it that the antidepressants generally prescribed for anxiety would significantly change this situation?
Ok, they might be swinging the lead, but so are lots of people. And if they were they'd probably let you prescribe them something. Things are crazy right now, lots of people are unraveling rapidly but this is temporary. I'd err on the side of kindness. In the words of Samuel Johnson, it's happier to sometimes be cheated than never to trust.
EDIT: Plus I'm guessing that any talking therapies you might refer them to have huge waiting lists and are hampered by having to operate remotely.