Can a man who is the biological father of a child avoid paying back child support if another man is listed on the birth certificate?

My husband actually had this happen to him. He had a one night stand with a girl before we were married. He never saw this girl again, until she showed up with a baby one day and said it was his. In the mean time, when she found out she was pregnant she married another man whom she thought at the time was the father. DNA test proved that my husband was the father, and everyone moved on. Years later the mother and the presumed father were divorced and the mother wanted to seek child support arrearage from my husband. This is a strange position to be in. If a man's name is not listed as the father, and someone else is then he is legally the presumtive father. Once the DNA test is done though and someone else is proven to be the father, they are responsible for child support from the moment they find out they are the real father. The guy listed gets off the hook and the real dad has to shell out what he owes. Trust me, it's ugly and I have lived through the very same ordeal.