2-Pieper:
Didn't mean to imply that most Damascus guns have Damascus ribs, just said "so many other period makers" did. I've seen a fair number of Damascus Parkers (and other makes) with Damascus ribs; but my own observations seem to indicate that fluid steel ribs become a lot more popular once makers began machine matting top ribs (obviously have no hard evidence, only personal observations; but Damascus ribs sure seem to the norm on early guns with unmated ribs).

And you are correct as to SAC's importation of barrel tube stock, as somewhere in my research stack I have a period article relating to SAC's introduction of their small bore (16 & 20 gauge) models in which it was discussed estimating demand as they prepared their overseas barrel/tubes order for the coming production period. But regardless the rib type steel used, it seems a bit far-fetched to me that a company such as Parker would allow their barrels to be assembled over seas. Although I am aware that some small and obscure American makers ordered in un-finished barreled actions for completion here in the states; unless it can be proven to me otherwise, I simply have to believe that Parker assembled their own barrels to include those with Damascus ribs at the gun works.