Gospel criticism

A common objection to the inerrancy or even general historical reliability of the Gospels is synoptic variants, where there are differing accounts of the same event (although in some cases these may be similar, but different events). One account words things differently from another account. One account contains details absent from another account.

Let's take a comparison. In this talk, Don Carson relates a personal anecdote:

https://www.youtube.com/watch?v=U21MquBWfag&feature=youtu.be&t=15m

The segment is between the 15-19 min mark. The anecdote is a combination of firsthand and secondhand information. He wasn't present when his wife prayed. Obviously, she was his unstated source of information for that. However, he personally knew the cancer patient and her husband. 

In addition, he has written about the same incident:

Not long ago in my church, a woman I’ll call Mary experienced a recurrence of cancer. Within a few months it had spread throughout her body, and despite treatment, she was very ill. The people in our church gathered for prayer. And although this is not a church from a charismatic tradition, the prayers throughout the day became more and more enthusiastic.

“Lord, you’ve said you will answer if two or three are in agreement. We have 287 in agreement, and we want you to heal her!”

“Jesus Christ is the same yesterday, today, and tomorrow. We want you to show that you are still the Great Physician!”

“Lord, will you not have mercy on her husband and her children?”

Finally it was my wife’s turn to pray (she who had almost lost her life to cancer twice) and she prayed, “Heavenly Father, we would love it if you would heal Mary. But if it is not your will to heal her, teach her to die well. She is going to die anyway, and so if the time is now, teach her to die well. Give her a joy of the Lord. Give her a heritage of godly faith, with one foot firmly planted in heaven, so that her husband and children will be stamped by it, and will look to Christ. We don’t ask that she have an easy time, but ask that she be so full grace, people will see Christ in her.”

Well, you could have cut the air with a knife. No longer were there 287 people agreeing in prayer. My wife’s prayer seemed to create a break in the chain. She was letting down her side. We found out afterward that some of Mary’s relatives rather wished my wife would go to heaven first so she would know whereof she was praying!

A few months later, Mary’s husband called me, and was desperate to talk. Mary’s health was going down and down despite every treatment conceivable. The church was wonderful, bringing in food, reminding them, “We’re praying for you . . . the Lord is faithful.” But he wanted permission to talk about his wife’s impending death. The heated atmosphere had made it impossible for them to talk in those terms, as if it would no longer be walking by faith. Mary couldn’t focus on eternity or talk about it, because there were so many Christians around her telling her she was going to be healed. D. A. Carson, "Dying Well," N. Guthrie, ed. Be Still, My Soul (Crossway 2010), 113-15.

http://s3.amazonaws.com/tgc-documents/carson/2010_dying_well.pdf

Compare and contrast these two accounts. Notice how the talk contains information omitted in the written version. This despite the fact that both accounts are from about the same time.  

Suppose we were to approach this in the same way critics approach the Gospels. Suppose we didn't know that both accounts came from the very same observer. And suppose there was a literary convention of writing in the third-person even though the narrator was an eyewitness to the event he relays. 

Imagine how critics would seize on the differences. Imagine how they'd ingeniously reconstruct the underlying sources. Imagine how they'd appeal to redactors to explain the variations.