I'm a little late to the party here, but I'll chime in anyway. Wood was used as a spacer because that's the way things were done at that time. It would have been painted with the bed and not covered with metal.
Jim Carters truck is a 1946 1-1/2 ton model. Most 1-1/2 ton Pickup Express models were delivered with single rear wheels so this makes Jim's truck extra unusual. The Rusty truck, which I assume is a '38, is also a 1-1/2 ton model.
The 3/4 and 1 ton Chevy trucks, from their introduction in 1937, use a regular looking pickup bed. It had smooth sides but was longer than the 1/2 ton version, but NOT 9 feet. For '37, '38, and '39, the wheel base was only 10 inches longer than the 1/2 ton. I don't know when the 9 foot pickup bed appeared on 1 ton model Chevy or GMC trucks, but I don't think it bore much resemblance to the 9 footer that was on the pre-AD 1-1/2 ton models.
Mike