Home School should be understood to be parent and child directed without interference from any outside authority.
The above article does a good job laying out the issues of the new ways the government run schools have been finding to make inroads in the direction of controlling the definition. Why? Because they seek to redefine home school enough to force it under the control of the government educational system, the same system most of us have fled because it is too broken to fix, too expensive and totally insensitive to the actual needs of our children!
Anyway, read the article, it is worth the time.