I just think they made better plywood back then. I know I found pieces of plywood in old houses and used in garages I know have been there for years and other than ragged edges it's all there. Leave a piece of plywood sit in your garage a few days and it'll bow so bad you could use it for a skate board ramp. I know, I have a new piece of 1/2" piece of plywood in my shed that I'll never be able to use for anything. If I were to replace the wood in my panel I'd sure strongly think about using marine grade.
Plywood in mine, too. The back corners had began to rot, other than that, it was in decent shape. Mine was painted black, both sides which was probably the original color. I'm told (can't confirm) the truck was a police paddy wagon in Canada when new which might explain the black. I bought a piece of 3/4 inch cabinet grade oak plywood. I painted the underside with marine polyurethane (6 coats) same color as the truck. Inside I used a sealer/stain then 7 coats of floor polyurethane, like you would use on oak floors in your home. I have a piece of carpet that matches my interior that I put over the floor if hauling things that might scratch.
I think Ford had their own lumber operation - They cut lumber in Northern areas of Mich and hauled it to one of their plants in Detroit where it was used for various body parts, packing crates and what ever else they needed wood for.
If I remember correctly they used their own thickness standards