The whole idea is, on its face, silly. It is, as you say, a gratuitous and unsupported fallacy. But the fact is, even if soldiers fearing imminent death while crouching in a foxhole did suddenly find god...what would that prove? What is the value of belief articulated only in the moment of extreme terror and trauma? Since you are a journalism professor, and apparently a great one, I offer an analogy to the reporters who apparently believe that they should get their sources drunk, so that they will talk more. But what is the value of that drunken talk? It may be literally nonsensical. Joe McGinniss tried this--not only was it gibberish, but he got drunk, too, and couldn't read his own notes the next morning.

I certainly do not speak for all those who have been in foxholes, but when I was 20 years old and in a good number of foxholes spread out over Vietnam and Cambodia I did not think of God at all.
Not one thought do I remember thinking about God.
I thought about the moments, not in a carpe diem way but in a get through this one and you are one moment shorter, one more moment lived through without losing anyone or body part, one moment closer to going home, where ever that is. I smoked a lot of cigarettes.

When I sat awake at night on guard I would think about America and Democracy and Freedom and Liberty and how those words changed meaning out where the rubber meets the road. When you are actually in a foxhole you are either digging it or using it. In neither case was God a factor in this soldiers young head even though I had been to Church, sung in choir, lit the candles and gone to Methodist Youth Fellowship every Wednesday for the years proceeding the foxholes adventures. I was just a young testosterone laden lad; Jesus did not follow me to Asia, he stayed home with the folks and the Church and the big organ.

The thing about foxholes is they are always a long, long way from anywhere familiar.