>Perhaps it's something like: families that earn enough to have one parent stay at home don't use child care. Therefore children in child care are more likely to be from less affluent families than those who are not in child care. So it's not the child care that causes the difference in outcomes, but just general income scale.

No, the OP speculated a variety of reasons, which includes what you've suggested, but I'm specifically focusing on the "which could be in the details of how care is provided and its quality", which is why I quoted that part specifically.