But this statement is entirely UNTRUE. I do not know where this person got such an idea but it isn’t true. The statement generally speaking, the Catholic Church does not consider civil marriages between baptized Christians to be valid isn’t accurate. In fact, it is just the opposite.
When two non-Catholics marry in some sort of religious ceremony, officiated by clergy, the clergy person is a LAYPERSON. They have no holy orders. There is nothing special about their presence or absence. The clergy person is the civil witness to the marriage, not the witness of the Church. The exchange of consent between the couple makes the marriage.
Whatever else they do, clergy or couple-- say a prayer, dance around and beat a drum, break a glass, jump a broom, sing a song, kneel, stand, or read reading out of the bible or the Twilight book, bless rings-- NONE of that has anything to do with validity. The non-Catholic clergy person has no ability to confer a blessing or confer a sacrament.
There is absolutely no difference between a couple exchanging vows before their clergy person and a couple exchanging their vows before a magistrate/justice of the peace. In both cases the couple is exchanging their vows before a layperson, who is simply a witness.