This is a really good question because in some cases the decision to camp illegally may be necessary to avoid a dangerous situation of trying to hike many miles further.
Yup, we've been lucky ..... except once. Got to the Osgood Tent site around 4pm or so, in the pouring rain no less, and all the platforms were already taken. This was in 1996, so I forget the exact details, but in this case we were ok because the area is relatively flat and we just walked off into the woods a little ways and found plenty of areas to set up a tent.
Had there been no option to set the tent up there, I'm not sure what we would have done. Since it was getting late and we were exhausted, I guess we would have either walked back aways down the Madison Gulf Trail or maybe along the Osgood Trail.
Our decision to not summit Madison that day proved to be wise. Sometime during that very day, July 20, 1996, the summit of Mount Washington, just a few miles away, recorded the record wind speed for the month of July at 154mph!!
During that night, even at the lower elevation of Osgood, we were constantly awakened by the roar of the wind, the snapping of trees, and even a few "thuds" of falling trees. One missed our tent by about twenty feet.