Alzheimer's and Memory

For some reason, wondering how much people are their pasts made me think of a study I once read about involving identical twins. Apparently scientists interviewed several pairs of identical twins who had been separated at birth, raised in very different circumstances, and found each other later in life. The twins were also shocked both by how bonded they felt to each other and how much they had in common. Apparently they shared a lot of interests and likes/dislikes despite never having met before. That makes me think that some part of a person is just innate and therefore entirely separate from memories. On the other hand, I feel that people are products of their circumstances to a large degree, such as most criminals being born in poverty and most fortune 500 CEOs being born to wealthy or at least middle class families. If those people lost their memories they'd probably be entirely different.
I'm not exactly sure how the article about Alzheimer's fits into this. I thought looking at the disease from a religious perspective was definitely an angle I hadn't thought about before. I like the idea that even if people with Alzheimer's can't remember things they are still touched on some level when one manages to connect with them and/or make them happy. Two summers ago, I volunteered at a nursing home. One women had very little short term memory, but she had enough long term memory to tell me she'd lived in several countries and could speak (or used to be able to speak?) quite a few languages. These languages included Hebrew and she'd spent quite a long time in Israel. When I sang Hebrew songs with her she would remember the words and her face would light up. I'd really like to think that even if she couldn't remember that ten minutes later I still brightened her day on some level. I think she was still the same person every day even though she couldn't remember things...but of course she did still have some long term memory. I'm really unsure about this.