RightWing,
I think you've got some terms confused - assuming the photo in the link that was provided is correct.
The tire is the same on the left half of the tread as it is on the right half. That means it is symetrical. Asymmetric means they are different - usually in the form of an extra rib.
And the photo shows a non-directional tire - no matter how you swap the tire around, it will always look like the photo. A directional tire has an arrow pointed look to the tread pattern.
BUT most tread designs have some sort of angularity to them that makes the look like the should come on pairs, but for practical purposes this doesn't really affect wet traction.