I would like to point out that when Jesus was baptized...the Holy Spirit alighted on him like a dove with the voice of God thundering...”This is my Beloved son in whom I am well pleased!” From then on the baptisms were to be of Jesus Christ which would symbolize the burial of the old man and the rising of the new man by the energizing work of the Holy Spirit! From then on the influence of John the Baptist would decrease while the influence of Jesus Christ would increase as John himself had declared it. Christ would indeed begin to baptize men with “fire and with the Holy Spirit”!
As for Mary, she was in obedience to the Law but she did not fulfill the law...the law was only fulfilled thru the person of Jesus Christ.
Mary and Joseph fulfilled the Jewish law requirements for all new mothers by her offering those sacrifices, just like you fulfill the requirements of the law when you pay your taxes to the IRS. That is what that quote was saying.