....but Roman forces sorted out other insurrectionists; I believe the head of the insurrectionist Thuedus was hewn and produced to the Prefect, and Pilate got himself into loads of trouble later on for the way that he handled an insurrection, causing orders for his return to Rome to face charges. Ergo, he would have been the right person to make a decision about an arrested and convicted insurrectionist.
Also, the fact that the Christian authors of the Gospels made such a point of explaining that Pilate had ordered the execution when it did not really suit them, seeing as how they tended to want to blame the Jewish leaders for Jesus's death, but they still left that report in........ a strong case for Pilate death sentence to have been genuine.
Pilate is reported to have sent Jesus to Antipas, but Antipas seemed not to care about Jesus any more because he was no longer in Galilee, and so he sent Jesus back.... all these reports do sound 'right'.
I cannot explain how stonings get mentioned..... would need an authority to throw light on stonings.....