I'm sure there are numerous sites in the Whites that are truely stealth. But, as you walk along, you will see many unoffical campsites very close to the trail.
For what it's worth, the Backcountry camping rules for the White Mountain National Forest say no camping, wood or charcoal fires within 1/4 mile of any hut, shelter, tent platform, cabin, picnic area or campground except at designated sites and any trail head as well as a few special areas.
The list goes on, but I don't see anywhere that prohibits you from camping right on the trail north of Mt. Moosiauke, provided you are more than 1/4 mile away from road, huts, etc.