Unfortunately i’m on the iPhone and cannot post links so I’ll have to wait until I’m on computer.
But it just isn’t as cut and dried as you project. There are multiple authorities who accept Josephus’ references. One does show some evidence of a little “doctoring” by subsequent Christian scribes (thanks RCC~) but there is little doubt that the entirety of the reference is authentic. This was done by comparing the writing style of the entirety of Josephus’ work. And many of these authorities are Jewish so have no vested interest in maintaining Christian tenets.
The site which you referenced has an obvious anti-bias, so their opinion on this isn’t surprising. But at this point in time there are far more authorities who accept Josephus’ references as valid than those who don’t so it isn’t a foregone conclusion as you imply.
But, in the end, we have a basic difference of opinion on the matter and I doubt that either of us will succeed in convincing the other.
Everybody has to make up their own mind about the historicity of Jesus.
But, when on computer, I will try to post a few links to back up my point about Josephus.