We got REALLY sick on our last trip too. Well DH didn't but me and our 3 DS's did. We caught a virus - most likely from Disneyland. It had a 2 - 3 day incubation period (I know this for a fact because our littlest was in the hospital and they were able to tell us exactly what virus we had via testing) and we started showing symptoms on day 5 of our trip. I think it is fairly safe to guess that someone in every group will probably get sick - there is the stress of travel, the sugary food, the late nights, large crowded areas... It's gonna happen. When it does it SUCKS - but I don't think there is anything that Disney can do about it. They have a great First Aid station and the parks are SOOO clean. (It makes our local fair seem so dirty in comparison) We used hand sanitizer too, wiped down the hotel phone and remote etc - bugs just happen so the best thing you can do is plan for it. I always travel with tylenol for every age group, cough medicine, tums, pepto etc because they are often more expensive or harder to get on vacation.
eta- That being said we brought our baby on our trip. We have travelled with infants before but never to somewhere so crowded and I honestly don't think I would ever take that chance again. We aren't the type to leave one at home, so I think if we are blessed with more children there will just be no big trips until baby is older. I thought about everything before we left, carseats, rides, rental strollers but not about him getting sick. For me, because he was dangerously ill, although we had a good time (and HE LOVED the rides) it just isn't worth that kind of risk.