It's not really a fair thing to say. It states that the owners of the companies were responsible for the end of child labor by paying workers more, but ignores the fact that workers were only paid more after minimum wage laws were passed by the states and US Congress, which were generally passed at the same time as child labor laws. Prior to the minimum wage laws, many workers were not paid well. One of President Roosevelt's comments in favor of the minimum wage law was, "No business which depends for existence on paying less than living wages to its workers has any right to continue in this country." Given that the two laws came at about the same time, it's not fair to say that owners paying their workers more money, which Rand and Hessen neglect to mention was mandated by law, was more responsible for the end of child labor than child labor laws.

I have a hunch that this question is probably better posted at /r/Economics or something economics-related. A considerable number of Nobel-caliber economists would likely take Rand's statement seriously in light of the nature and extent of their economic understanding, which historians might or might not also possess.