And I agree; it turns out that planets are really heavy and have an incredible amount of inertia; moving some asteroids around isn't going to cause the Earth to slip on a banana peel and fall into the sun.
The original article about placing 416 Earth-sized planets in a stable orbit does involve a quantity of mass greater than Jupiter (at 317.8 Earth masses), but building habitats out of what we have available in and inside the asteroid belt is a much more modest scope.
Not that I disagree! We also have the Hilda, Trojan, and Greek asteroids (in Jupiter's Lagrange points) to work with. The Jovian and Saturnian moons too. It'll be a long, long time before we need to worry about dismantling the gas giants themselves.
On our path towards maximizing the livable land area in the Solar System, I wonder what we will run out of first. It looks like water, iron, carbon, etc. are all pretty abundant. We'll run out of* some rarer element (like Phosphorous or something) before we ever approach maximum constructed land area.
*And by "run out of", I mean even with perfect recycling, the spot market demand for the material maintains a price level where it's uneconomical to develop further, barring discovery of new supplies or more efficient usage.