You can't reduce the drag on a clean aircraft but you can increase it, that's why I'm saying its not maximum drag. If you are going for a maximum speed, the drag is actually as small as you can get it at that speed, minimum drag.
Your quote from Pete Swatton, who is usually careful with his words:
"The maximum speed is achieved when maximum thrust is equal to the total drag"
He does not say 'maximum drag', he says 'total drag', which is exactly correct.