There's no record of Winchester buying an old battleship, but there's no doubt that it could easily come into a LOT of such steel on the secondary market.
Between 1920 and 1925 the US Navy sold 17 of its pre-dreadnaught and dreadnaught battleships to ship breakers for scrap in response to the naval arms treaties that were being enacted.
I think a similar number of cruisers were also scrapped, as well as several ships that were partially constructed.
Here's the only problems I have with this scenario, though...
Winchester was making barrels out of nickel steel as early as 1905.
Armor plating of the time was nickle steel, normally face hardened using the Harvey Carburization process. Very high quality steel for the time, and VERY expensive, even on the secondary scrap market.
Winchester would very likely have purchased such steel already blended to their specifications, and I really doubt that they'd go overboard in the nickle content, as that kind of steel is a LOT more expensive.
The problem of receivers getting the funky bluing cast normally cropped up after 1964, when the manufacturing process was changed.
What I don't get, however, is why Winchester woudln't have made the entire gun out of this steel, and I also don't see Winchester, or any company for that matter, laying in a 25-year supply of steel.