Not at all. The pp was referring to the process in respect to genetics. Throughout a pregnancy and at the time of birth the baby’s mother is the woman who carried the baby. There is no “genetic/egg” mother, otherwise any woman who has a baby with an egg donor for medical/fertility reasons would have to go through a legal process after birth.
At a subsequent time, babies can have another legal mother, through (what should be) a well organised legal process, but of course they will always have a birth mother - the woman who carried them, not the egg donor - and a legal mother.
This is not to in anyway diminish the emotional connection a legal mother might have, or elevate the connection a birth mother who was otherwise disinterested. It is merely to point out the legal basics of a surrogacy arrangement to highlight that a genetic mother doesn’t have rights. This is important for discussions around the legal mess that any surrogacy arrangement causes. It’s not personal.