The only reason that these children in question are "legitimate" is that their mothers have lied to the courts. Doesn't this constitute perjury?
Techically, no.
First, the assertion was made in a delivery room, not in a court of law, while under oath.
Also, there are no laws that I know of that CRIMINALIZE the act of listing the wrong name of the father on a Birth Certificate. The law has recognized that for many women, they have no idea who the father of their child might be.
Some list no father's name at all, but for those wishing to recieve Welfare for their child, it is MANDATED by law, that they list the father, so that the State can enforce support payments against him.