I understand that the Sadducees denied the Oral Torah, but to me Josephus is saying that this had little impact on their judicial rulings. In other words, they tended to do the bidding of the Pharisees.
I'm not saying that the Sadducees in the Sanhedrin were asked to kill Jesus for breaking the Oral Law. I'm saying that the accusation of breaking the Oral Law was one of the reasons that the Pharisees used to get him arrested and brought to trial and ultimately killed. So even in the NT, Sadducaic judges, though perhaps not without a little muscle flexing on their part, nevertheless played a part in the process that led to Jesus being killed like the Pharisees wanted. I think this is a perfect illustration of what Josephus is saying.
And not everyone in the Sanhedrin was a Sadducee (e.g., Gamaliel the Pharisee in Acts 5:34):
"The two leading Torah personalities at the end of the Second Temple period were Rabban Yochanan ben Zakkai, dean of the Sanhedrin, and Rabban Shimon ben Gamliel, of the family of Hillel, the Nasi. Of the two, the undisputed leader was Rabban Yochanan ben Zakkai. He counteracted every attempt of the Sadducees to tamper with the Halachah. The importance of his success in this defense of the Torah is highlighted by the fact that the Sages proclaimed as minor holidays the occasions when Rabban Yochanan defeated his Sadducean opponents. In his capacity as president or Nasi of the Sanhedrin, he participated in the central government, and led the political opposition to the treacherous conduct of Josephus in the Galilee. The Sages, led by Rabban Yochanan and Rabban Shimon generally supported the political line of the more moderate Zealots in their reisistance to Rome. However, when they realized that because of the internal conflicts and wars there was no chance of withstanding the Romans, they chose to take the initiative in a daring action to save Jerusalem and the Holy Temple from total destruction. Rabban Yochanan pledged non-involvement in the revolt to Vespasian in return for three things: "give me Yavneh and its sages [to reconstitute the Sanhedrin]", the family of [Hillel] Rabban Shimon ben Galiel should not come to harm, Vespasian should provide a physician for the R'Tzadok, the tzaddik of the generation who had been fasting and praying that Jerusalem and the Temple should be spared from destruction. [HOJP I, p183-184]"
http://www.thesanhedrin.org/en/index.ph ... Roman_rule
The Oral Law was essentially the law of the land and the Sadducees could only persuade the rich:
"And concerning these things [the Oral law] it is that great disputes and differences have arisen among them, while the Sadducees are able to persuade none but the rich, and have not the populace obsequious to them, but the Pharisees have the multitude on their side" (Ant. 13.10.6).
"... they [the Pharisees] are able greatly to persuade the body of the people; and whatsoever they do about Divine worship, prayers, and sacrifices, they perform them according to their direction; insomuch that the cities give great attestations to them on account of their entire virtuous conduct, both in the actions of their lives and their discourses also" (Ant. 18.1.3).
So how did this state of affairs affect the rituals of Sadducaic priests? I suppose they either had to be willing to die for their beliefs (as some were, according to Josephus), be flexible, or run off to the desert like the Dead Sea Scrolls sect. But those who were willing to be flexible were "able to do almost nothing of themselves," and "when they become magistrates ... they addict themselves to the notions of the Pharisees, because the multitude would not otherwise bear them" (Ant. 18.1.4).
"...the Pharisees have delivered to the people a great many observances by succession from their fathers, which are not written in the laws of Moses" (Ant. 13.10.6).
"These [Pharisees] have so great a power over the multitude, that when they say any thing against the king, or against the high priest, they are presently believed" (Ant. 13.10.5).
And the Pharisees used this power with the Herodians, the chief priests and the Sanhedrin to kill Jesus, and their influence with the people persuaded them to choose Barabbas instead of Jesus (all from Mark):
"Then the Pharisees went out and began to plot with the Herodians how they might kill Jesus."
"Then the chief priests, the teachers of the law and the elders looked for a way to arrest him because they knew he had spoken the parable against them. But they were afraid of the crowd; so they left him and went away. Later they sent some of the Pharisees and Herodians to Jesus to catch him in his words."
"Very early in the morning, the chief priests, with the elders, the teachers of the law and the whole Sanhedrin, made their plans. So they bound Jesus, led him away and handed him over to Pilate."
"The chief priests accused him of many things."
"But the chief priests stirred up the crowd to have Pilate release Barabbas instead."
The Pharisees had their hands on all these levers of power (like Josephus says they did) and they used them to kill Jesus.
And Pilate is presented as understanding the real situation:
"Pilate, knowing it was out of self-interest that the chief priests had handed Jesus over to him."
But even he is presented as being powerless to stop it:
"Wanting to satisfy the crowd, Pilate released Barabbas to them. He had Jesus flogged, and handed him over to be crucified."
This all seems more powerful than having only veto power.
Searchlight casting for faults in the clouds of delusion.