I've never seen a share option before :s strange request in my opinion, poor pup I hope it does find a great family!
i do beleave that is their situation, but they are wanting dog sitters but dont want to pay for them. they will be wanting to pick a choise when the new family gets to keep they dog.But it could be what it is.
Someone with a young baby who really doesn't want to give up their dog but knows they can't keep her as they do.
Charging can also "deselect" the wrong people just taking her.