Not everything. Not by a long stretch. Please see false dichotomy.
I'm at home in the back yard.
I have three visitors.
1.) The Probation officer knocks on my front door I don't want him to know I'm home so I sneak off and hide in the bushes hoping that if he comes back he won't see me.
2.) My neighbor knocks on the door. I don't care if he knows that I'm home. I don't care enough to go to the front and let him know I'm home and I don't care enough to hide in the bushes. If he sees me fine. If he doesn't fine.
3.) Heidi Klum knocks on my door. I jump to my feet and run around the house with visions of sugar plumbs dancing in my head.
It can't be said that I either want my visitors to know that I'm home or that I don't want them to know that I'm home.
Your argument is demonstrably fallacious.
I disagree. If for some reason the Law of the Excluded Middle doesn't seem to apply, it's because the predicates haven't been adequately defined.
When you say "Not wanting someone to know is most certainly not the same as not caring if one knows", you're using an inexact, though common, sense of "not wanting someone to know" that basically equates to "wanting someone not to know". Technically, however, "not wanting someone to know" describes everything (including but not limited to complete indifference) other than actually wanting someone to know. So formally speaking, not caring one way or the other is a subset of not wanting.
That is, I believe, what Hyver was getting at, and he was correct.