I thought Kenshin's sword actually had the blade on the reverse side, that was the point. If he sliced you without thinking about it, it wouldn't draw any blood. He also couldn't do his whole quick-draw jazz if all he was doing was holding it in reverse.
The blade IS on the other side, take notice of the hamon (the tempered squiggly line). The shininess might have thrown you off because a lot of artists tend to use that to show sharpness but that's not the case here.