Yes, they are, assuming they're made of oak. Not all of them are.
I am not fond of oak, in spite of the fact that we happen to have several antique oak pieces of furniture (book cabinet, hall bench, library table and china cabinet) in our eclectic home.
My first Gerstner, the large one that will accommodate a 24" rule, was made of (solid) mahogany, which I didn't particularly like. It was purchased new for the handsome sum of $75. This was back in the spring of '58. You can see what has happened to the value of the dollar, considering the same box, today, is near $2,000.
I've always liked walnut, so my current one is made of that, and it, too, is solid. The only thing that isn't walnut is the drawer bottoms and the hardware, as well as the wool felt that lines the box and drawers.
Tom commented about rusting on chisels. Yep! If the wood used isn't completely dry, you can expect rusting. Note that in tool boxes, the tools are not in direct contact with the wood.
H