Originally Posted by relentlessflame
We already know that there is a gap between when you "die" (your HP hits zero) and when you disappear, because we've seen many occasions where people put in last words, and even move their bodies around a bit. We also know that there was a resurrection item mentioned earlier in the anime that allowed you to revive someone for up to 10 seconds after they "died". So yeah, "death" isn't instantaneous. And even after you disappear in the SAO world, it doesn't necessarily mean you brain fries right that very second either (or that it's instantaneous). We can assume that, after Asuna disappeared from the boss room, she was sent to the sky platform, to await Kirito who followed. Perhaps this is because this was all part of the end-game sequence, and they were the designated end-game players... or perhaps it was simply what was set to happen to anyone who is killed by the GM.
Rewatching the scene I have to agree that that was a bad translation and it was Kayaba turning off his immortality. Kayaba only promised that he wouldn't let her kill herself right away. Technically, she didn't kill herself. Kayaba did. If her Net Gear hadn't fried her, then she's still there at the games end so the kill mode may not have been operating. It was never explained how long it was between game death and real death AFAIK. Kayaba also gave her credit for helping to end the game, since Kirito was dead meat at that point.
Finally, it's just a question of whether you have a "willing suspension of disbelief" to accept what happened or not. I do because I accept the premise that Full Dive capabilities and self aware AI exist so other anomalies that would not be possible in today's games could also exist. Your mileage may vary.