My guess is that Disney is more than accommodating if you show up at the port and say that you have been sick in the last 72 hours and they ask you to not board the ship, but I'm not surprised that if you call the day before and say that, that they insist on a cancellation fee. There is just too much liklihood of fraud and people who cancel at the last minute just calling and saying that they are sick. The policy does seem backward, but it does make sense.
I think what Disney needs to do is have a big hot pink letter in your docs that say "if you become ill within 72 hours of your cruise, please follow these instructions" and include seeing a doctor and have a doctor fax a note about your symptoms. This, of course, could be abused as well but at least there is a policy in place to deal with the situation before someone arrives at the port only to be told they can't get on the ship.
As far as the cancellation insurance goes, my guess is that if Disney refuses to allow you to get on the ship, your cancellation insurance would kick in regardless of the reason (hence you wouldn't need a doctor's note).
Even so, frankly I am guessing that someone who has a sick child and is vigilant about hand washing and keeping them out of contact with other kids is probably not the reason for the outbreaks last year. Have you seen the bathroom habits of people? SO many people do NOT wash their hands when leaving a bathroom (or give a quick rinse). If people did that then there would be a much smaller likelihood of ANYTHING going around and they probably wouldn't have to ask if people had been sick in the last 72 hours because things wouldn't spread like wildfire.