I would have tossed the sheets too. You don't know why this family's son was sick, so I would play it safe.
I would have made a claim against the damage deposit (don't know if that's what you did for compensation). Yeah, **bleep** happens, (sorry, couldn't resist), but good sheets are expensive. I buy high quality ones and I would have been really annoyed.
The thing is, we're small business people, not big hotel chains. I don't think we can be expected to pay out of pocket in the same way given we don't enjoy the same economies of scale. That's something I wish more guests understood. Staying in an Airbnb place is often a lot cheaper than staying at an expensive hotel, especially for a family. Part of the risk guests take is when they damage property, even inadvertently. They shouldn't expect us to absorb costs in the same way.