Yep, there were a lot of stories, but no officer or NCO or anyone else in wartime had the authority to sell or give away U.S. government property of any kind. Even if a GI lost has rifle and had to pay for it on a statement of charges, he could not "find" the gun later and keep it. I have heard all those stories, some many times, but they are all untrue. The only weapon in the U.S. military that was actually given to an individual soldier and was his to keep was the General Officers' Pistol (different kinds at different times). Those were the personal property of the general, and could be legally kept after he left the service. (After the war, duly authorized property disposal officers could sell off specified types of materiel, but that was strictly controlled when it came to weapons. If a rifle, why not a tank, or a B-29?)
I had a personal experience with one of those stories. I met a young man whose deceased father I had known well. He told me that he had his father's M1 rifle that General Patton had given the old man for his bravery at the Battle of the Bulge. Patton was going to award him a medal but the soldier told the general that he would rather have the rifle he had used to such good effect in that battle. Patton gave the order, and the GI was allowed to bring the rifle home. It was a touching story.
There were a couple of problems. I had known the father before the son was even born, and knew that he had never been out of the states in WWII, let alone at the Bulge. And I had been with him when he picked up the DCM M1 at the Railway Express Office. In the bosom of his family, the vet, like others, had "expanded" on his wartime service.
No, I didn't tell the man; it made no difference to me to let him think his father was a combat hero.