There are many reasons why a family might want to home school for a limited period of time and then send a child back to public schools. This is an option that parents always have available to them. In fact, it provides some parents a sense of security. You can try home schooling and if it isn't quite working out for your family, the kids can still go back to the public school.
In the final analysis, the public school would one way or another determine in which grade to enroll a previously home-schooled child. Generally, the public schools will go with the grade they deem appropriate to the child's age unless they have hard evidence that the child is incapable of doing school work at this grade level (evidence such as standardized achievement test results.) Public school officials would probably be reluctant to skip a child ahead (of his age group) academically, even if a young scholar's accomplishment would seem to urge this. They would be more enclined to provide an "enrichment" environment for such a child instead.