OK, I think that it is really ironic that Rose takes Oliver in when she does know that he was "probably" part of the robbery. She does have a pre-concieved notion about Oliver. It is correct. He has had a lot of bad luck.
I am happy that he has had three months of nurturing and love shown to him by Rose and her Aunt. I do wonder what is going to go wrong with this picture.
Oliver does show that nature overcomes nurture because he wants to go visit Mr. Brownlow and the housekeeper. He is saddened by the fact that they have moved to the West Indies. Why have they moved. Maybe it is because he doesn't want to face the fact that Oliver is a thief and he is his grandson. If Mr. Brownlow has money, which he does, taking himself away from the situation would make it easier.
Spark Notes stated that the "inquisition" of Oliver at the Aunt's house was just like a courtroom. The great thing is that he did have a say and he was believed to have given them the truth. This, hopefully, gives Oliver a little more self-confidence.
Spark Notes did say that the parallel of Oliver being accepted into the "family" of the Aunt and Rose was also supported by moving to the countryside.
Charles Dickens, in my opinion, is an optimist in this book.