Almost Persuaded. Why?

As a musical accompaniment to this discussion, I am linking to the Louvin Brothers' rendition of the traditional hymn "Almost Persuaded."  A most remarkable singing sensation from the 50s and the early 60s, though nearly forgotten now. Although I like their music, I'm sure I would differ with them theologically. This is from Lewis's Surprised by Joy: 

Then I read Chesterton's Everlasting Man and for the first time saw the whole Christian outline of history set out in a form that seemed to me to make sense. Somehow I contrived not to be too badly shaken. You will remember that I already thought Chesterton the most sensible man alive "apart from his Christianity." Now, I veritably believe, I thought — I didn't of course say; words would have revealed the nonsense — that Christianity itself was very sensible "apart from its Christianity." But I hardly remember, for I had not long finished The Everlasting Man when something far more alarming happened to me. Early in 1926 the hardest boiled of all the atheists I ever knew sat in my room on the other side of the fire and remarked that the evidence for the historicity of the Gospels was really surprisingly good. "Rum thing," he went on. "All that stuff of Frazer's about the Dying God. Rum thing. It almost looks as if it had really happened once." To understand the shattering impact of it, you would need to know the man (who has certainly never since shown any interest in Christianity). If he, the cynic of cynics, the toughest of the toughs, were not-as I would still have put it — "safe," where could I turn? Was there then no escape?

Now, why would an "outsider" like this "hardest boiled of all the atheists I ever knew" think that the evidence for the historicity of the Gospels was anywhere near being surprisingly good? Because, in the ancient world, when there is a strong mythological element, you don't find the people who present myth providing lots of times, places and dates. Supernatural claims are not typically embedded in carefully constructed writing aimed at conveying reality. Myths do not occur in recorded history, and stories like Apollonius of Tyana, for example, include things like Apollonius showing up in Nineveh seven centuries after it had been demolished.