The rationale is this: board is not a fixed cost. The student has to eat wherever he is living. The costs of the parents home, "room", is fixed. Neither the parents or the student are out of pocket, for room, when the student lives at home.
But, you are right, you won't find that in Pub 970. But, the bottom line is: you are limited to the school's "allowance for attendance" (or "allowance for cost of attendance") which is usually less for students living at home.
