There are several places in the US that this actually happens which in all reality is NOT fair for the non parental person here. Now if they volunteer to help, its one thing but to be mandatory by Law to do so is completely wrong
Unless they have adopted the child, or became a legal guardian in some other legally binding way, IMO they shouldn't have to pay. However as Arthur Wright has stated in some states in the US, if you have been supporting the child and you and the custodial parent split, you will end up paying child support.