The South won while Stonewall Jackson was around. Once he was shot (mistakenly by his own men) the South began losing. You need to qualify that slightly. The south won more frequently in the east while Jackson was around. The war in the west was marked by defeat after defeat for the confederate forces. But you are correct that once Jackson was killed, Lee never won again.
I don't know where people are reading their history these days, but it's hard to believe the Wilderness is considered a Grant victory. Perhaps the New York Times is the source.