So it becomes part of you by integrating into your DNA? It's only going to be a fraction of your cells that contain that DNA. I don't see how that makes it any more you than a virus that doesn't integrate. Herpes stays in your system for life, and doesn't incorporate into DNA.
OK, that's an interesting case that I didn't know about, but it just shows how blurred the lines between genes, virus and transposons are. This is a virus that you can pass on to your children, but not others around you, correct? It's not what I was considering when taking about viruses, because of the infectious element. You have shifted my mental boundary about what is considered a virus.
It looks like think something that is part of your genome is part of "you" - I won't argue that it isn't, it certainly is from one point of view. I don't plan to have children, so I have a different perspective on things.