Trying to locate a SciFi story for someone

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On another forum to which I belong, someone has posted the following request. If anyone here can help identify the story and/or author, I'll get the information back there.

It reminds me of a science fiction short story I read maybe 40 years ago, and that I would love to find again. There was a world war going on, and everyone was expected to dedicate their life to the war, becoming a 'hardened and sharpened tool'. Casualties with 'nuclear shell-shock' were disappearing from their hospital beds, and returning saying they had traveled back in time, but being too disoriented to give constructive help in diagnosing their condition. When told they should pull themselves together and help the war effort, they simply disappeared again.

Top brass wondered whether this could be used for military purposes: sending troops, supplies, or even just information back in time to where it was needed. To analyse the situation, they found a history professor (in jail for insufficient commitment to the war effort).

The historian realized that the patients were reporting false history, and that they were disappearing not into the past, but into a world of their imagination. By this time, a funded project had been set up, so this setback was regarded as an obstacle to be overcome. The historian suggested that disappearing into one's imagination was the province of poets. "Find me a poet!" ordered the general in charge, but all the poets had been turned into hardened and sharpened tools, so the war was lost.

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I've been told that "Disappearing Act" by Alfred Bester is probably this story.