Doesn't state approved home schooling (in the USA) usually include aptitude testing at a local school? My impression was that the curriculum was set by the school, and the teaching was done by the parent.
Not universally, but laws vary widely by state so there may be somewhere that that's true. In our case we have a once a year peer review session to go over what we did but we choose all the material ourselves and aren't given any particular material or requirements from the local schools.
There's an expectation that we are providing an education, but until our kids want to enter the system in one way or another, they won't be tested against its requirements.