It's impossible for me not to care at all--on a computer, I am constantly making small changes in word choice or in small additions or deletions that I might not even consciously notice. But the goal with "zero draft"--a term I got from someone in my workshop--is to get the words down as fast as possible by focusing on the story rather than the crafting of the prose.
Of course,"story" and "prose" are inextricable in a way which I'm not sure I can explain, as it's something I feel is true. But at the same time, "story" can be pared down to mean simply "things that happen" and "characters they happen to." That's what I'm doing now. I'm writing scenes that I think ought to have happened to my characters, in order to see if their behavior in those scenes seems consistent and interesting. I think of zero draft as "figuring stuff out on the page."
The important bit is that all this crap I'm writing is subject to change. If it doesn't work, out it goes, no harm, no foul. Some things I'm writing now might linger in the manuscript for a really long time, only to be cut when I'm almost done. That doesn't matter. Those words will have served their "figuring out" purpose.
That's one thing I learned from writing the last novel. I'm going to cut tens of thousands of words, possibly as many as fifty thousand, over the course of writing a novel of maybe 100,000 words. So I might as well not stress too much over wordcount while I'm figuring things out.
At the same time, large wordcounts give one a sense of accomplishment that's hard to beat. And figuring out seems to take more words than refined, edited prose. I'm stopping action and writing down infodumps, made up on the spot, for my own information. I'm describing things that might be peripheral to the scene going on because I realized I know what something ought to look like and I don't want to forget about it. And I'm writing scenes that I might not need to show in the final product; they might be backstory, or irrelevant except to my backbrain.
So. Zero draft, whee!