i wouldnt take on the responsibility either for many reasons. one, im not trained to do so. two, the other kids in my care would suffer as well since i would not be able to do the things that i also do with them such as swimming/skating lessons, drop in playgroups etc.
i also have always said that i wont take in a child that would change our lifestyle and family too much as in a peanut allergy since the peanut butter is a staple in my home.
i think that this family is trying to find a cheaper way to care for their child, i seems to me they may be trying to take advantage of your kindness.