See My Thread On P-Marked Stevens Shotguns
If interested, see my similar thread of about a year ago.
https://www.milsurps.com/showthread.php?t=35891
I have two Stevens shotguns with only the P marks on the top forward receiver and top rear barrel, no other military marks such as US, flaming bomb and another P near the bomb. Best guess at this point is that the guns with the upper P marks but no other military marks were Blanket Procurement Program items that were not used by the military directly, but stored away or perhaps diverted to related activities, such as use by civilian guards at non-military installations having importance for the war effort. But I have as yet seen no concrete verification of this. I think it is reasonable to infer that they are most likely authentic WWII military-related marks and not some type of post-war Bubba fakery, though.