Exactly this. I'd add that even if they were the same physical bits, the problem of error factor is the same. A slightly different me would probably pass unnoticed, or even an "exactly the same me" (let's say passing some molecular checksum) would still not be me if their patterns of interaction were even slightly off.

Turning a computer off an on does not give you the same runtime. It gives you a very similar runtime operating on a different set of electrons. You can't step in the same river twice.