If I were your brother, there is no way that I would agree to pay child support without a paternity test. Look at it this way: There is proof that the woman is the mother of the child since the baby was born from her body. What proof is there that your brother is the father? Absolutely none.
And she may not be going for child support right now, but she will be. If she is on any kind of state aid, such as welfare, subsidized housing, TANF, the state is going to go after the biological father for child support. Even if he signed the birth certificate, he is not legally the father according to the Courts since he was not married to the child's mother.
If they had been married, the child would legally be his even if he were not the biological father since all children born during a marriage are considered to be the legal child of the husband.
I think every time a child is born, unless it is known to be the result of artificial insemination or something similar, there should be DNA testing to prove that the "father" is indeed the father. There are a lot of cases of paternity fraud where a woman will claim that the man is the father and he will find out years later that he isn't. And I'm a married woman who knows for a fact that my husband is the biological father of my children.