Jason, was the person who tested positive named on the reservation? If not, how would one even know if the claim is true?
I would say if either the origin country or the BVI blocks travel, or the person named on the reservation tests positive. Reason being, what if they book a ticket through SXM or somewhere that blocks entry, that shouldn't be your problem, anymore than the guest's relative gets Covid. That's what trip insurance is for.
It was a child so I doubt they would have been named. Interestingly, the poster had insurance that would have refunded 75% but she was beating up the charter company because she wanted a full credit to rebook later. I have an issue with the timing of only 4 days notice. They were planning to not bring the infected person but she thought the other guests being exposed (but negative) should be reason enough to rebook.