They're compatible and contradictory at times. One of the most effective purposes of religion is to explain what what science can't, or won't.
Regardless, I think the premise of this story is invalid. He seems to use the argument: "Well, he must have done something to deserve crucifixion" as the cornerstone for his piece.
Seems to me that justice and injustice are doled out disproportionately, unevenly, unpurposefully all the time. Why would Jesus' crucifixion have to result from a just sentence?

It's not that it would have been a "just" sentence only that the Romans used crucifixion for certain crimes and not others. So, most likely, someone who was crucified was "guilty" under Roman law of one of those crimes. The person may have been completely innocent in fact, but found "guilty" by the Romans. Also, there's a LOT of room to say that crucifixion in and of itself was brutal and injust no matter the guilt or innocence of the victim.

I don't think the author's intent was to claim the sentence was just, only to ask what was the charge that triggered the sentence.

It had to be because Jesus (allegedly) claimed to be the King of the Jews. It is after all, the only charge that Pilate asks Jesus to answer in all four gospels. It's doubtful that Pilate cared whether or not Jesus committed some kind of blaspheny against the Jewish God. That may have been a serious charge in the minds of the Pharisees, but it wasn't something that would get you executed by the Roman authorities. Claiming to be the sovereign ruler of a portion of the Roman Empire would.

Now, whether or not Yeshua actually made that claim or whether being the Jewish messiah meant to him what the Romans thought it meant is completely different issue.

The Roman Empire was a juggernaut; a military, political, cultural and economic juggernaut. You had to play, pay or get out of the way (which were choices that were not necessarily mutual, nor definitely mutually exclusive). Repeat after me: GLOBALIZATION?. Good bad or indifferent…that is the question.

Justice? That is the answer. Justice for the widow, justice for the poor, the meek, the dispossessed,… jeesh...get it?