I doubt they had the luxury of manufacturing deliberately smaller-bored rifles - exigencies of war and all that.
This is probably a mutation of what happened after the war. Many of these guns were rechambered for the 30-06, with no other modification. No problem, other than lousy accuracy since the bores were 7.7mm (.311 cal.). The basis of this story probably came from those idiots who rechambered the earlier 6.5mms to 30-06.
Some years back the American Rifleman has an article about this. A gunsmith sent in some pictures of a REALLY elongated bullet, along with this tale: "A guy came in and asked me if I could make his gun shoot with less recoil. He complained it 'kicked too hard'. I nearly had a heart attack when I saw this 6.5 Arisaka was rechambered to 30-06. I have heard the Arisaka was a weak action but after seeing this I had to change my mind - the gun was still in sound condition after squeezing a jacketed .30 cal. bullet through a 6.5 (.266 cal.)tube."