  Sam, The proof usually consists of using a gravitational analogy of Gauss' law for electrostatics. But, an intuitive approach is basically like what you suggested.
Choose any point inside the shell, choose a direction, and form a cone around the line from the point to the shell. The solid angle of the cone will intercept a certain area on the shell (and therefore a certain amount of mass).
Now, go in the opposite direction and form a cone of the same solid angle. The area intercepted is proportional to the square of the distance from the point to the shell, and, therefore, so is the mass intercepted. But, the force due to the mass is inversely proportional to the square of the distance. The two effects cancel and the net force due to the two areas intercepted by the two equal solid angles in opposite directions is zero. Now, just integrate over the whole 4pi steradians!
And now back to our regularly scheduled topic. Thanks, Glenn

