It's not that I doubt the tale, exactly. It's just that, well I'd never heard it before, but I had/have heard John McCutcheon talk about and sing his trenchant (sigh) ballad, Christmas in the Trenches, about a real event in the FIRST winter of the war, the first Christmas, in 1915, when it all might yet have ended.
"My name is Francis Tolliver, in Liverpool I dwell"
Each Christmas come since World War I, I've learned its lessons well
That the ones who call the shots won't be among the dead and lame
And on each end of the rifle we're the same...