Petfinder cannot possibly screen the many thousands of rescues listed there, other than asking a few requirements of a group before allowing them to list.
Petfinder is just a listing service, and they do their best but unless someone complains, they have no way of knowing who is operating in a less than reputable way.
How much under 8 is your child and how small is the dog you were interested in?
Many small dogs are not patient with little kids and can be fearful and/or nippy with them. An 8 year old child should be okay with a dog who is known to be good with kids.
The Petfinder listing will indicate if the dog can go to a home with children.
Also, cute small dogs usually get many people interested. I would contact the group again and ask them what's happening with this dog.