Is Sarang a complete idiot?

[humanoid]

Step into a Star Trek Teleporter. You are teleported to the planet below. Did you die?

Yes. But at roughly the same time an assumably exact copy of you was created somewhere else, thinking that its you and acting like its you.

As for the question whether that copy actually is you, thats in my opinion up to oneself to decide, I don't think that there is a definite "scientific" explanation that would clear this up.

After all this is still all science fiction, it would take an actual working technology of this (teleporter and/or brain "copier") to decide which is the case because then we would (hopefully) know all the facts behind it.