I knew the factoid that Smithy-BM gets on average 4 Provinces in 14 turns
Do yourself a big favor and forget this factoid along with all functionally equivalent ones.
Well, I think the reason why I called it a "factoid" in the first place was to underline the point that, even if true, it might not lead to a valid argument. In any case, I am not sure it is wrong to wonder how much better Catacombs is than Smithy in situations like this. Now, there is a point that I was focused on the question "is there a way to get 5 Provinces faster than 14 turns?" which ignored two points that have previously been brought up here by Awaclus:
1) It's no good here to fail to contest Peddlers, and
2) There is a Bishop in the kingdom, and you can augment/supplement the original idea via the alt-VP route.
You emphasize the point that (2) is really key here because, yes, even if it does turn out that Catacombs-BM can grab (I'm making this up) five Provinces in 13 turns, Bishop can more than even the score so long as the game doesn't end too soon. And since (by hypothesis) the BM player has none of the Peddlers and never buys a Bishop, it's not going to end well for him or her.
One question on the example game:
A game I played yesterday neatly illustrates this concept: http://www.gokosalvager.com/static/logprettifier.html?20150212/log.514b5511e4b0b79c883b5e3b.1423793350871.txt
Chapel-Embassy-WV-Tunnel can make for a nice deck in a 4-card kingdom, but it's just hopeless in this particular 10-card one.
I think I have seen you opponent post here in f.ds before once or twice, so maybe there could be some clarification there, but the thing that really surprised me most here was the systematic choice not to buy Worker's Villages (you won that split 9-1, and it did seem to help :-)). And then also, sure, why no Bishop?