I’m not aware of any historical evidence that contradicts what you just wrote. There is basically no evidence that Jesus was killed by the romans for rebellion. There’s a lot of CONJECTURE, but no historical evidence. And in order to accommodate such a conjecture, you have to throw out known good reliable historical evidence.
In fact, there's no historical evidence to the contrary.
Regardless of the Gospels efforts to white-wash Pilate, the facts remain that by Roman law, only Pilate could order a crucifixion, and that only for a Roman capital crime, such as rebellion.
There is also non-biblical historical evidence that Pilate was a callous, cruel and uncaring ruler, for whom executions without trial were matters of routine.
That's why historically speaking, there's no evidence to suggest that Jews killed Jesus.