It is a very well-known story among Black people, so I think that he could have admitted that it originated with Booker T. Washington. Perhaps he read it long ago, who knows. But the story that he tells is too similar to be a coincidence. Plagiarists do not admit they have copied a story, ever. In a scholarly paper, recognition should be given by the author to the person with the original story. That is what footnotes are for.
He does not have to say "This is my original idea" to be a plagiarist.
The reality is that school janitors do a lot more than sweep the floors. They replace fluorescent tubes, they work with some pretty toxic cleaning chemicals, including Sulfuric acid for unclogging drains, they change filters in the AC, the cut the grass and do all sorts of handyman types of jobs. Many of these jobs ate too unsafe for children to do. If some kid falls off a ladder and becomes paralyzed for life, or is poisoned by dangerous chemicals, the school district is likely going to be sued for a lot larger amount than they would save by replacing the janitors with children.
Booker T. did not have to replace fluorescent tubes, he did not have to unclog a toilet with acid or lye, he did not have to use industrial strength degreasers or insecticide.
I see nothing wrong with having some schoolchildren sweep school floors and do simple cleaning jobs around the school. But no, you cannot replace all, or even most, school janitors with children.
