Surely in the US too there are laws about that kind of thing, even if the American government obviously wouldn't make a legal case out of parents homeschooling their kids.

As I understand it from the articles (if you can read German, I provided the links elsewhere), when the parents' case in court was dismissed, the father caught mention somewhere of a possibility of losing custody. The articles aren't much clearer than that about just how realistic that possibility is, what criteria have to be met before it's allowed, or whether any government service ever seriously considered that option - other than the mayor stating that no, they haven't. Considering the political fallout of such a decision, I would be strongly inclined to believe him, but I didn't see anything about guarantees, no (would be rather absurd to make guarantees, too, don't you think? If removing custody is a serious option, they can hardly guarantee not to do it, and if it's not a serious option, they'd only look foolish making guarantees that they'd never do it.)