Ill disagree with that statement. The tension (pull) side is just that, under tension so there is no slop there as its fighting resistance from the valve train. Look at a bike or motorcycle chain under load, its straight. By taking up the whip of the slack side, your doing nothing to the timing except controlling the deceleration portion whip where the crank may overrun the cam speed and tension the slack side for a moment, there is your timing variance. Load the valve train up and shake the slack side, nothing is going to move. I'd run a tensioner and I'd even run a stronger silent type chain on it with its smooth back: nothing to dig a groove into the teflon slipper and about 200% more contact area on the cogs.
