I understand what you mean by this, but I wonder: In some areas is "unschooling" actually called "not schooling"? Are they the same thing? Something different?
I ask because a couple of months ago I heard a mother describe her homeschooling style as "not schooling," and I don't think she meant it in the way that you do. At least, I can't imagine someone boldly proclaiming to a group that she is actively choosing not to educate her children. This occurred at a planning meeting for a new co-op, where we were all introducing ourselves to the group. I had to slip out before the meeting was over, so I didn't get to ask her what she meant. Others introduced themselves as "unschoolers" so I don't know if there is a difference.
FWIW, the meeting was absolutely a free-for-all, and I knew when we left it wasn't the group for us. (I don't do well with chaos, lol!) Kids were literally running all over the room, screaming, jumping off furniture (did I mention we were at the library?). One kid, about 6, repeatedly interrupted the meeting by running into the circle of adults and demanding everyone's attention, while his mother sat there and giggled. That's my only experience with un(not?)schoolers, and I'm not willing to lump them all in the same category, but it's clearly not the style for us.