How interesting.

After two lbs's told me I had as good a chainline as one could expect, I put my Pista up in the garage workstand and gave it a long and serious eyeballing.

As I eyeballed the sprocket, I noticed it had a flange around the hole for the hub, but only on one side and not on the other.
I speculated that flipping the sprocket over would move the sprocket over, about an eighth of an inch closer to the centerline of my bike, and thus give me a perfect chainline.

So, I rode down to the lbs that sold me my Pista, and which also assembled the bike for delivery.
Why, yes, they had put the sprocket on backwards.
With a little encouragement from me, they flipped the sprocket over and I now have a perfect (I mean perfect) chainline.

I need to invest in a lock ring wrench and a chain whip so that I don't need other people to keep my bike rolling.
I should start a thread asking for a minimum tool and parts list to keep my Pista (and me) happy.

-----

Anyway, during the eyeballing phase, I noticed my Armadillos have an arrow on them and the words "direction of rotation."
If I put a sprocket on the other side of the hub, so that I could change sprockets by flipping the wheel, that would change the direction of rotation.
Does this matter, or, did the Specialized folks just put the arrow and the words on the tire to make it look more "specialized"?