So the Vatican is not in any way a source for the number of Catholics?
The number of true Catholics? No.
The term "Catholic" is often used loosely in the media. The Vatican can tell you how many people attended Church on Sunday. It can tell you how many people have been baptized. It can tell you how many people checked the "Catholic" box in the national population census. That's what is usually meant by "Catholic" when statistics are discussed. It's based on self-identification or numbers of people who have had some form of contact with the Church.
What the Vatican can't tell you is how many people actually believe what the Church teaches.
And if one does not believe what the Catholic Church teaches, then one is not a Catholic.
There's nothing unique about that. If you believe in God, then you're not an atheist. If you don't believe in Marx's dogmas, you're not a communist. If you don't believe in Calvin's teachings, you're not a Calvinist. Irrespective of where you plant your posterior on a Sunday or any other day.