It seems to me you are under the impression of sudden media like today. It took a long time for widespread media at the time. They didn’t have social media, nor print presses. Every thing had to done by hand. Spreading the information within that time seems very accurate for the time. And Josephus died at 63. Not a big gap, but still a gap compared to what you’re saying. He was born around 37 AD (4 years after the death of Jesus). You’re telling me that he couldn’t have got real explanations of it through his life? If we’re going to say that, then all the people born a few years after WW1 are lying