i'm not convinved yet.
It's true that it could be one of those "war stories." I'm currently reading a book about Jean Laffite, of Battle of New Orleans fame, and it's very discouraging to see how many of the long-accepted stories about him are not supported by any documentary evidence.
The same thing happened when the recent "definitive" biography of Stonewall Jackson came out.
In the case of Gen. Pershing, if this is a fiction, it seems to be a fiction composed contemporaneously. He was a distant relative of my late grandmother, and there's no doubt he was a toughie.