Of course we know that wasn't the Doctor in "Astronaut," but the point is that the perception of the Doctor being dead only works if being fatally shot while regenerating actually would kill the Doctor. If regeneration were a guaranteed ticket out of any and every form of death, then his enemies would never have believed they'd succeeded in killing him.
Nagisa, I'm not sure if a bullet to the brain would be a guaranteed kill; we're not talking Sylar here. (Or Claire Bennet, I should say, since Sylar stole that power from her.) Maybe if it were the kind of bullet that tore up the insides of the target with fragmentation and shock waves, that would do it, but if it were a more limited brain injury, it might still allow regeneration. But if he were, say, blown apart in an explosion, or burned up in a fire, or something on a comparable level of bodily dissolution, then yeah, there'd be no coming back from that. (Granted, the Master somehow came back from being vaporized in "Planet of Fire," but I've always taken that to be an aftereffect of the power he stole from the Source of Traken -- which could also explain his ability to survive in gooey snake form in the '96 movie. He wasn't technically in a Gallifreyan body at the time but a Trakenian one, and of course he still had the same face and voice after his, err, recovery, so it doesn't count as a Time Lord regeneration per se.)
