Legally, maybe. In practice it's usually impossible to get 200 feet off the trail anyway. At least if you ever want to find it again. You can't even see 20 feet off the trail in most places.
The only sections of the AT through NH where it is practical to find a place to set up a tent are in low elevation areas, lower then 3000 feet or so. And there isn't much of this. Most of the time your either going steeply up or down hill or above tree line. In the dips between climbs its a bog where all the water collects. Any "flat" area your likely to find is a bed of wet and spongy moss. Then there are all the down tree limbs and rocks.
That's why there are a large number of developed campsites with tent platforms located in the areas where it's practical to do so. To suggest that people can camp along the AT through the Whites and avoid the AMC sites is just plain irresponsible because it really isn't a practical thing to do, even in the few places where it might be legal to do so.