I don't even know if I can put this into words right now, because the idea just struck me, but here's for trying, anyway. . .

I used to think that Sirius was dead, and Dumbledore is alive.
Now I'm thinking, what if neither of them are dead?
I think maybe Dumbledore just needs Harry to think that so that Harry will have the anger he needs to kill Voldemort.

Maybe Sirius doesn't have to be alive for this theory to be true, but it might explain why Dumbledore wanted Snape to "kill" him so badly.

I know it might not make a whole lot of sense at this point...oh well.