Hawk -- great point!!
I think I got myself into trouble when I stated "he's responsible for the first RUN that scores, regardless of WHO scores it."
I was trying to paraphrase the rulebook and shouldn't have done that.
Here's what the OBR says: "Rule 10.16(g) Comment: It is the intent of Rule 10.16(g) to charge each pitcher with the number of runners he put on base, rather than with the individual runners. When a pitcher puts runners on base and is relieved, such pitcher shall be charged with all runs subsequently scored up to and including the number of runners such pitcher left on base when such pitcher left the game, unless such runners are put out without action by the batter (i.e., caught stealing, picked off base or called out for interference when a batter-runner does not reach first base on the play). For example:..."
And then in gives 7 different scenarios -- one of which is the one I originally posed.
From re-reading, I'd say that if P1 walks a guy and P2 induces a FC resulting in R1 -- once the bases are cleared (as you suggested via DP), at that point P2 is on his own. So in the scenario you posed, I'd say P2 gets the loss.
Good find!