But that doesn't sound nearly as cool or media hype-able.

I meant to say that there would be zero days between when I could patch my (hypothetical) Windows machine, and when people could start hacking it. The Wikipedia article you linked elsewhere seems ambiguous, e.g. "It is called a "zero-day" because the programmer has had zero days to fix the flaw (in other words, a patch is not available)." Microsoft has had something up to 90 days to produce such a patch, but hasn't for whatever reason.

Actually, 0-day refers to the time since public disclosure.