The reason non-welfare cases were allowed under the act is because it was assumed those cases created a risk of an obligation to provide public assistance if payments were not made. This risk would only be present in cases where the state agency can demonstrate that pecuniary interest. The purpose of the guidelines suggested in the P.O.P.S. case to "sustain the child at a standard of living concomitant with her divorcing parents' income" is contrary to the expressed purpose of the federal act, and was improperly borrowed from the purpose of alimony in an action under common law when the breadwinner abandons his family. It it not the purpose of title IV-D awards.
A private civil law case is one that does not affect a public monetary interest. This is why non-welfare cases cannot be classified as "all other cases." The P.O.P.S. case did nothing to expand the proper reach of this program to all other cases, or "give" jurisdiction where none existed. The fundamental right to be left alone, where there is no public interest in recovering or avoiding costs incurred under public entitlement programs was not upheld by this decision. The plaintiff's due process and equal protection arguments were simply and properly shot down.
The law was interpreted by the Sullivan court when they proclaimed title IV-D was meant to work in tandem with title IV-A of the act (now TANF). Any interpretation contradicting this ruling is political rhetoric. You really should read the case.