It sounds like everyone is arguing about semantics. What is considered the actual "birth date"?
I'm a web developer. What is considered the birth date of a website? When the client comes to me with a proposal or I go to them with one? If I was Berners-Lee, it sounds like that is the birth date of the website. If the site is ready for internal testing, is that the birth date? That sounds like what CERN says it is when it was available internally but possibly not externally. Or is the site's birth date when it's publicly available, ready for the world to see and use, which is what I would call it.
Or putting it in human terms, Berners-Lee's birth date sounds more like the date of conception, CERN's date more like when you have an ultrasound and you know it's there and can "see" it but it's not ready for the world yet, and publicly accessible when the little guy actually shoots out of mom.