Why was the involvement of Pontius Pilate questionable?

The idea that the Sanhedrin or the Council of Jewish Elders condemned Jesus and took him to Pontius Pilate to be crucified was unrealistic since the Sanhedrin could have issued a death sentence as well as Pilate. Also, Pilate's offer to free either Jesus or Barabbas seemed unrealistic as Pilate would not have to make such an offering to the people.