You didn't follow that link's argument very well. Gravity is negative energy. Each body's gravity exactly cancels the energy of its mass. I believe the concept originated with John Archibald Wheeler's group back in the 1940s.
At any rate, the point is that the sum throughout the universe is zero, but locally there can and do exist positive amounts. Gravity is the balancing negative.
How can that be? Gravity is the work you have to do to haul masses apart. It's a work/energy deficit.
Drop an anvil down a dry well. You get seismic waves rippling away. You get sound. There's energy released, but that's only because there was energy stored in having the anvil up out of the well in the first place.
Want to do it again? You've got to do work amounting to the potential lost when you dropped the anvil down in there.
Energy exists. Something that says otherwise is wrong.