This says it all right here, folks.

[Major Nikon]

65. I don't have a negative view of the series

The fact that it's published by PBS almost certainly means it's of high quality. However, regardless nothing about him can be taken as factual which you suggest, even his own existence. For all we know he could have been entirely made up and there are biblical historians (albeit the minority) who have suggested as much.

There are those who claim Jesus said or did this or that. In doing so they are just trying to pass off speculation as fact whether or not they realize it. Everything he said or did is 4th person and decades after the fact at best by the time it made it to written form.

What's more important than realizing much of the story is demonstrably false is asking why someone lied about it to begin with. The Bethlehem account is a vital part of Jesus' story because it establishes his messianic claim. An educated reading of the canonical gospels reveals Jesus never claimed to be a god, only the messiah. Pretty much all of his messianic claims fall apart on close examination and not just the Bethlehem part. Even if you were to assume Jesus was the messiah, this means he could not be a god as the Jews considered those two things very different. Had Jesus claimed to be a god during his time, he almost certainly would have been executed sooner than he was as this would be a blatant violation of idolatry laws and would have been view even less favorably than a false messiah. There's really no reason to even consider him as the messiah. Even most Jews of his time rejected as much.

The idea of Jesus as a deity came much later, and even some Christian denominations to this day reject it. That whole idea came from early Christian theology perpetuated by the Catholic and later Protestant church. There's no hard biblical evidence for it.

The reality almost certainly is Jesus was little more than a streetcorner preacher who enjoyed a bit of success during his lifetime, but his legend and surrounding mythology grew much larger.