What does this tell you about this mother? She has a little girl in the USA, but does not put her fathers name on the birth certificate for legal purposes only because she does not want the father to have legal rights over her daughter. He father will not know about her until she is 18 years old. If the laws in the USA are the same as in Belgium or in Italy (where most parents will never have to deal with family court), than her father would be able to see her and will not have to pay child support if he does not want to. The mother does not want to deal with family court in the USA and it does not matter if she has a good father or not. Otherwise she would have allow her daughter to see her father with out going to court, and she will not ask him for child support. She also does not want the father to go to court and prevent her from moving out out state/country with her daughter or get a US passport.
Answer on What does this tell you about this mother?
If i understand you right. The mother wanted a child but no strings to the dad. I don't agree with it but if she is able to do it and the father doesn't want any part of his child. Then that's their thing. Not my place to comment on it. If the father wants involvement with his child then the mother is wrong for what she's doing.