Methinks you're exactly right! The fact that the little girl was not admitted to the school may have had nothing to do with the two women she lives with. It sounds as though they just wanted it to be that way, and ran with it!
There are many reasons why kids don't get into Catholic schools. Are the women she lives with members of the Parish to which this school is attached? If so, are they CONTRIBUTING members? The school has every right to limit who gets in to those families who are supportive of the Parish. Once all those are in the school, then the Parish will open the school to other Parishes who will do the same thing. If there are still openings, then the school will consider other Catholic or non-Catholic children. Regardless, the school has every right to deny a place to any child.
This is the first Register Guard article on this. If you still have any questions, give a holler.