That's just one of the errors; the entire account has problems with accuracy. But in all honesty I think that the best evidence that it is all imaginary is the fact that Douglas Southall Freeman mentions Lee's wartime servant in passing in his biography, and it wasn't Willie Mack Lee.
Lee’s servants during the war are pretty well documented, not least in the letters that Lee himself wrote. He started the war with one servant, Perry, as his body servant and another, Meredith, as his cook. Later Meredith left and was replaced by George. They were paid $8.20 a month each. Lee mentions them often in his letters back to his wife.