Actually, that report includes a few examples of children killed on the job. Like a 16 year old who died while working in construction, he fell about 160 feet to the ground after trying to jump from a roof to a nearby powered lift. In Nashville. [2] (same link as [1])
It also details the rise in children being employed to do hazardous labor.
Killed in sawmills is a bit of hyperbole, but it's not far off from the truth it seems.