@Dan:
I did google "joseph michael ocasio" and found the details of that case are a bit different than the hypothetical situation in that the paternity issue wasn't raised for many years (13 years after the birth of the child).
Ocasio
I also thought income was a factor and that if Dad got a paycut he could file a motion to have his payments decreased?
Anyways, perhaps this situation is plausible and perhaps not, it probably depends a lot on the judges involved. The court could order a DNA test done and the mother would have to submit.
That's not to say the laws shouldn't be changed, just that this scenario is probably a bit over the top.