"Hah! What are you going to do? Crucify us?"

It was an event in Caesar’s youth; we actually don’t have Caesar’s own account of the story, since only his Commentarii on his later wars (and some letters) survived the past 2000 years.

It would be a difficult thing to fake, however, considering he was a young no-one at the time, that he had little political clout with which to ‘back up’ such a tale, that the locals and the governor would have every reason to contradict him if it was false, and that his political enemies would have used such a bald-faced lie to sink his political career.

I don’t doubt that in Caesar’s verbal retellings of his heroism, he played up the drama as much as he could. But regardless of the details, the event almost certainly happened broadly as stated - he was almost certainly abducted by pirates, paid a ransom, and then, on his own initiative, collected and led a militia force to capture and crucify them in revenge.