No, I do not agree with anything in the article except that Christ was not born on December 25. First, to address the date. In Luke, Zacharieh, father of John the Baptist, was serving as in the order of Abijah as Chief Priest, which, according to records, had duty on the week of June 25 or 26. John the Baptist was born nine months later or in later March. We know from Scripture that Christ and John the Baptist were six months apart in conception, which puts Christ's birth in late September.
As far as the year goes, two words at the start of the article raise an automatic doubt. Those words are "the Pope declares." Most anything written by or recorded by Catholic hierarcy is based on the agenda of the Catholic Church, not Scripture or the purposes of God. I will go with historical records that existed before the Catholic Church came into existence around 500 AD. On top of all that, the author claims the 4 BC date is wrong, but cannot pinpoint a date other than "it was much earlier." Really, what can one say about an entity that used to create false genealogy charts to justify the birthright of kings.