Actually, I was just referring to the comment that we were supposed to be struck by how offensive Don was in the scene and how he managed to weasel his way out of anything--I guess I should have quoted it.
It's no problem, don't sweat it :-) The thing is, I really don't hate Don. I think he's a fascinating character. I don't even think that he would be purposefully cruel to a family, and take their dog, thereby wreaking some emotional havoc, to put it mildly. It would break my heart to smithereens if someone took my dog, and Don Draper wouldn't purposefully smash a stranger's heart to smithereens. However, he does sometimes allow himself not to think about things like that.
When Dick Whitman took Don Draper's identity, he did so not knowing about Anna Draper, or allowing himself to think of things like that. He saw an opportunity, it was to his benefit, without actual malicious intent, he did what he felt he needed to do. The real Don Draper could have had four kids waiting for him at home, never knowing why daddy just never came home. He didn't, but Don didn't know one way or another. I also don't think that's about "well screw them, mwhahahaha!", I think Don is incredibly skilled at putting things like that out of his mind. "It will shock you how much this never happened."
So I think the possibility exists that Polly was someone's dog, but that Don, without actual intent to inflict emotional injury, just wouldn't have thought of that family, those kids, their feelings if, at that moment, he saw a dog and deemed it the necessary part of the equation that was missing for whatever complex reason.
But I don't think it is about "Well, then he must suck, is evil, twirls a mustache, robs nuns..." but rather this man has a complexity in what he is trying to find, that an otherwise feeling person, sometimes just goes for it.
I don't think we will ever know for absolute sure. It's strange, because I find it one of the more intriguing mysteries about Don and worked on me in a way the "is he reaching for a gun? No, oh good, it's cash...whew." thing didn't because Weiner never ever, supplied the "whew" just the "Wha...?"