I agree ! To me it seems that they are looking for the cheapest and easiest solution to meet their needs so that neither of the parents would have to lose their job or that they wouldn't have to pay a nurse or nanny more.
What better way to save money than asking your existing daycare to take on that responsibility.
I am sure they are stressed and were not expecting to deal with this issue but I really get the feeling that they are putting too much trust in a daycare provider and thinking about what is cheapest and easiest for them rather than what is in the best interest of their child