It might be a replacement. The seller never shows a good picture of the strap right against the main body of the bag so it's hard to see if the leather colors match exactly. I've never seen that style of strap used as a Coach-made replacement on anything except one of the airline versions of the Stewardess.
It's interesting that you ask this question now as I just got a classic pouch with the same strap! We know this strap was available as we have seen it on stewardesses made for the airlines. The one I have is the same length as the strap on a stewardess and the one in the listing seems the same. I don't recall any retail bag that came with a two sided strap that buckled on like this one. It's possible that Coach offered it for new bags for a short period of time but that seems unlikely since we would have seen more of them. It's also possible that the original straps were damaged and Coach offered these as replacements or that an enterprising SA offered them to her customers. Since we don't see them often, it probably wasn't a corporate policy.
Thanks to both of you. This is my first Courier Pouch. I'll be interested to see how closely the strap matches the color of the bag.