No, that didn't confirm that the original was killed. Just that an extra body was created from the original pattern.
That's up for interpretation I suppose, but I always interpreted it to mean that transporters are basically the same as food replicators. They don't need to reassemble people using the exact same material that goes in, which is why it was even possible to glitch out and make two Rikers. Either way, no human can survive being reduced to elementary particles, so whether they are remade with the same stuff or replicated stuff is moot. It will always be the case that a person who is disintegrated by a transporter will die, as all of their neural patterns and internal organs are utterly annihilated to a degree as severe as if they were at the epicenter of a nuclear explosion. A few seconds later, (or a minute later, or a year later, it should make no difference) another being is deliberately assembled to imitate the original down to every minute detail, and it is now that this new consciousness
begins its life, albeit with the memories and birthmarks of the original person. But they are no more the same consciousness as the original than the two people in the OP's example are, and for the same reason: one of them is dead!
Except that in the Trek 'verse, they demonstrably have dualism.
If they didn't, then they couldn't have switched souls between bodies. They couldn't put someone's 'consciousness' into a bottle then decant it into Spock, Kirk an d Love Interest. They couldn't have Spock and Chapel sharing consciousness.
So there was, like ryan fantasizes, a non-physical element that WAS the person, that somehow traveled along the beam to be the real person when they put it back together.
It didn't travel in some methods that made copies (such as the android who retained Kirk's racist remark, and the sci3ntist who said: "I'm real, ask me the square root of your zip code! I mean, i can math like a real boy! No, wait, i mean..."), but the transporter allowed it to.
Otherwise Dr. Janet Lester would just have been crazied in her own head, no matter what the technology was trying to do.
It would have been interesting if they had an episode where the bad guy used one of those 'consciousness switching' technologies, and he was foiled because everyone who's been transportered was technically without a soul and immune. "Nener, nener, Doc. Now, get into the shuttle or well beam you to the brig."
But for the Trek verse, more likely would be the episode where the technology was working and the only people who were immune to the effect were Data and one of the two Rikers. Then a lot of self-indulgent dialogue about 'All this time i was sure _I_ was the real Riker.' The real one would, of course, be the one who became XO because there's no way the crew, Troi and the audience would have been made to reevaluate their feelings for suddenly-the-copy-Riker. That would have had ramifications far past the one and only episode, so they'd avoid it.
syllogism.
