I find this idea quite interesting. You say that our memories aren't our memories (in the title of this post), but aren't they more OUR memories if the act of remembering adds part of current you. I guess the question is what makes you, you. Memories? How we are now? How we were? What we have done? I think an interesting comment to add as well is that humans have a tendency to be cognitively dissonant. That means we can have inconsistent thoughts and memories because of our changing behavioral and attitudes. It's basically when we do something in the past, that we now believe at the present to be irrational, and so we think up of a new reason why we did it (rationalizing that past decision and changing your memory of what really happened). While this phenomenon is not exactly the same as the one you described, they're both part of how our brain changes its memories over time.
Maybe I was being too careless in my wording. Our impression of what memories are, is wrong. Your memory of a situation is actually a re-enactment of that situation, that you are undergoing now. When you remember that situation again in the future, you are re-enacting the last re-enactment, not going back to the "original memory" and remembering it again. .... and thinking about that just makes me want to write some Philip K. Dick sci-fi...