Not 100% certain, but believe, that in the scenerio you mentioned above, the relief pitcher is credited for any outcome except a walk.Because the previous pitcher departed game with two or more balls in count, he would be responsible for the walk.
That's my inclination, but the bigger question is why? The pitcher coming in is going to pitch differently to the batter being down 2-0 in the count. I just think it has to be the original pitchers line score no matter what. I may be wrong, and I probably am, but I would like to know the rule and the reasoning behind it.
Not certain of the exact reasoning behind the rule, but I think you can divide potential outcomes into three categories:(1) Batter makes an out (RP clearly deserves credit for recording the out)(2) Batter safely reaches base, excluding walk (Technically, RP is more responsible for outcome than SP...Even when you factor in having to pitch differently because of the 2-0, 2-1, 2-2, 3-0, 3-1 or 3-2 count) (3) Walk (This is credited to SP because SP put RP in position where walk was a very likely outcome)Perhaps the shark move for a stat-hound RP would be to walk the inherited batter on purpose...Knowing that runner (and potential ER) would be credited to SP.