I don't think anyone is suggesting that Dr. Williams is a liar. But he is an economist and not an historian, and he has fallen victim to the well entrenched southron myth-machine. Take this quote from the article you posted the link to, "After the Battle of Seven Pines in June 1862, Union soldiers said that "two black Confederate regiments not only fought but showed no mercy to the Yankee dead or wounded whom they mutilated, murdered and robbed." Very straight forward, two black regiments among the rebel army. OK, here is a link to a source listing the confederate order of battle for Seven Pines. Every regiment, every brigade, every commander. Which were the two black regiments? It's a simple question and one which should be easy to answer. Go for it.
No.