It sounds like they do, although I admit I am a smidge more sympathetic to the homeowners than I am to H4H. As new homeowners (and I am assuming that they have never owned their own home before) they were probably dealing with scores of challenges that they had never faced before. It was up to H4H to make the determination that they house was safe. Its not a "buyer beware" situation like most of us deal with. When we buy a home on our own, its up to us to look the house over and decide if we want to pay an inspector to look the house over even better. H4H is supposed to do that on behalf of the people its helping. From what I've read here, they dropped the ball. Anytime you see standing water in a basement, the very safest thing you can do is assume that there is mold, find it (you will!) and have it tested. The testing is not cheap. In our area it can cost up to $5,000. However, the one-time expense of testing is far less than the long term cost of treating a fmaily that has been living in a house with toxic mold.
In case you hadn't guessed, I really can't stand H4H or its peanut farming cheerleader.
I like H4H, but they certainly dropped the ball here. The family sounds like whiners, but they really have a problem and sick children to boot! Toxic mold is a major problem and I can't imagine that any organization in the housing field would let any living creature into a structure with standing water without testing it!!