Actually, the examination of a suspect by a Roman official was an official government act. There would have been guards present, as well as a government scribe who would take down a transcript of events. (And if the person was famous, there would probably be a fair number of rubberneckers, either in the room or just outside it.)
Most accounts of the trials of Roman martyrs seem to have been based heavily on transcripts from official records, augmented by personal descriptions by spectators of the martyrs’ demeanor. (It was common for a few Christians to attend trials and executions, the idea being that the martyr would see them in the crowd and be encouraged, and that the Christians could try to retrieve the bodies afterward. Of course, occasionally the Christians in the crowd would give themselves away or be recognized by hostile folks, so it was risky.)
Anyhoo, it does seem that only Jesus could have related the story of His temptation, as the Devil probably wouldn’t want to and you can’t believe anything he says.
Re: fitting into the Gospels literarily, let’s think about it. Isn’t Jesus always being approached and questioned and tested by all sorts of people? In this case, it’s a fallen angel instead of a Pharisee, scribe, Sadducee, Roman, or chief priest. Also in this case, all sorts of visual aids replace theoretical questions. But it’s still a game of “Stump the Rabbi with Bible Questions,” and it’s still someone trying to find out who this Jesus really is. The point of the story is that Jesus isn’t in league with the Evil One (remember, some people thought he must be healing and exorcising through the power of Beelzebub), that Jesus isn’t doing what he’s doing for any worldly display or power, and that he’s not under the Devil’s control in any way.
Jesus still doesn’t come out and say, “Oh, yeah, I’m God,” but as Jude pointed out by referring to the story about the Devil trying to get Moses’ dead body and St. Michael having to fight him for it, even the greatest prophets had done some kind of sin and were subject to the Devil’s power in some way. Except Jesus.
The other interesting thing is that with most of the prophets, we have stories of how they met with angels or with God, and received messages from them. But since Jesus already was God, we see different things happening with Him: the voice from nowhere at His Baptism giving a message
to the people, Moses and Elijah coming to consult with Him at the Transfiguration and another Voice of God
instructing other people, angels talking
to the Apostles and disciples.after Jesus’ Resurrection and again after His Ascension. So the temptation by the devil is yet another example of how Jesus doesn’t need to get instructions or gifts of power from an angel (in this case, an evil one). Instead, He instructs the devil like a rabbi instructs an erring student.
So my contention would be that the story of the temptation in the wilderness does fit into the Gospels.