For a pig receiver is simply doesn't matter where the flat side is, or if you use a concentric reducer instead of an eccentric reducer.
On the other hand, if you ever have to reverse flow in the line (e.g., Gas Marketing finds another place to sell gas that requires reversing some lines), then it matters a lot. Pigs can be heavy. In a launcher, you lay the pig in the barrel and shove it into the throat. With the flat side of a eccentric reducer down, the pig just slides. With the flat side up (or with a concentric reducer) it can be a serious problem to load the pig in the throat so it will launch properly. Stiff pigs (like the ubiquitous Turbo Pig) are often too stiff to be able to manually push them very far into the throat. With the flat side down, the pig will sit on the threshold of the throat and usually launch fine, with the flat side up, the pig will be cocked in the threshold and will probably not launch at all.
So, if there is never, ever, any possible chance that someone might reverse flow and require your receiver to become a launcher, then it doesn't matter. If later on someone needs to reverse the flow for reasons that you can't imagine at design, then you have created a wildly unnecessary problem for that future operator by not putting the flat side down.
I'd go ahead and fix the receiver right now. But then I've had to reverse a couple of dozen lines over the years.
David