The crux of the "this kills you" argument is that you're not being reconstructed from the same atoms: they're different atoms, your consciousness ends and a perfect copy made from separate atoms starts existing elsewhere. This is regarded as death.

IMO, the idea of "ownership" of your atoms is an evolutionary hurdle that needs to be overcome. Whatever fundamental particles this matter is being broken into/made from would have to be interchangeable. Therefore, I'd argue that the "pattern" of these things is what's important.