This would be trivial to do with one-time-pads. A bit bulky, but simple. But in a way, you'd still be right. The "dummy information" is (encoded into) the second key.
Several philosophers have attended to those very thought experiments. I recently read some of Locke's "Essay Concerning Human Understanding" (Book 2), and he has some interesting thoughts on person-hood and persistence of consciousness in chapter 27.