I make light fun of it with my friends and say "crap, he ded. Oh well, Poke Center ho'!"
But it'll always be fainted to me. It's fainting for a reason. If your pokemon DIED then you wouldn't have that pokemon anymore. Not to mention it wouldn't be able to be revived from death. That's just creating a ton of zombie problems we don't need right now.
I like to think that fainting is just that. The pokemon fought so hard that it fainted or has no more stamina to fight. It's like with the anime. The pokemon pass out on their side with swirly eyes then the fight is over. They're not dead, they just got the wind knocked out of them.
And the Poke Center lets them get some rest, and revives are like energy drinks. It's just silly to say they're really dead, unless you're playing a nuzlocke like -weeper- said.