I think the reasoning is wrong here. Obviously a tower could be stable, but still applying force to an edge of the top could make it collapse.
What's actually happening is that at each step, you already have a max-overhang tower of N bricks, then you add another brick below, to produce a max-overhang tower of N+1 bricks. Because the old N-brick tower is stable, you can place it anywhere on the new bottom brick as long as its center of gravity is not off the edge of the new brick.
What's actually happening is that at each step, you already have a max-overhang tower of N bricks, then you add another brick below, to produce a max-overhang tower of N+1 bricks. Because the old N-brick tower is stable, you can place it anywhere on the new bottom brick as long as its center of gravity is not off the edge of the new brick.