This is a great example of men turning existing paternity law upside down and giving it a good shake. Historically, any child born to a married woman was legally presumed to be fathered by her husband.
Welcome to modern times.
The other man is right to want the truth since the woman would demand support from him once her husband gets enough of her shit and shows her the door.
But also, and more importantly, if he is a father, he has a right to be a part of his child's life and he should demand and pursue that right aggressively and within the law. You can't be charged with harrassment for asking for what is yours as long as you stay within legal boundaries.
If this woman's husband took the same liberties during their "separation" and fathered a child, she would have to get her mind around the fact that her family is no longer the same neat little package as it was before. Her husband would be legally obligated to support another woman's child. Her children would deserve to share family events with their half-sibling.
She is assuming a privilege, an entitlement, to bring a child, possibly conceived outside of her marriage, into hers and her husband's home and raising it while excluding the father from their lives.
Justice is supposed to mean equality before the law without regard to gender. This other man has rights and her attempts to smear him as unstable etc. should be seen for what they are.