I think his checkered stocks issue is that he may be thinking of BRITISH ordered guns from early 1940-April, 1942, which did have checkered grips with silver medallions. After April, 1942, barrel lengths were standardized at five inches (for UK orders) and smooth stocks with dull gray finishes appeared.
Some commercial M&P's were bought by the govt. prior to the Victory Model, and they had checkered stocks, too. They were supposed to be for a Navy civilian police corps, but it never formed and the guns were used elsewhere. I wouldn't be amazed if some found their way to USN and USMC aviators.
I carried a number of former USN Victory Models in the USAF in the 1960's, and not all had Navy markings. I think quite a few unmarked Navy guns exist. Serial numbers may confirm them, or if you have one, listen carefully late at night and one may sing a sea chanty.