well... I'm not so sure that it has to do with restrictions so much as it has to do with contradictions.
Like if you say the child shouldn't hit other kids, yet you hit your child.
also stuff like bullying, controlling, and other abuse immediately disqualifies you as a healthy parent...
"freedom to learn things on their own" is not exactly sufficient since a parent who violates the property of their child can then allow the child the "freedom" to go out into the world and learn what happens when the child does not respect others' property rights. That's not healthy parenting.
anyway, that's what comes to my mind from my own experience with parents who weren't terribly restrictive, but not healthy.