While I highly doubt the existence of another “Earth” on the other side of the sun, the explanation given does not hold water. That explanation would have to assume the other planets have no effect on “opposite Earth” and only affect this Earth.
In truth if there was another planet in some kind of synchronous orbit with Earth, the other planets would exert an equal and opposite action. Sometimes drawing it nearer and sometimes farther from Earth, not just always bringing them closer together.
Theoretically, there could be some such orb.
Nope. See post 35 for the diagram. The article gets it right. The point directly opposite the earth would be the L3 Langrange point. That point is unstable in the direction tangetial to the orbit. That means that a planet at that point would stay put if the earth, the sun and that planet were the only bodies in the solar system. They are not. Peturbations from other bodies would lead to the planet moving just a bit ahead of the L3 point or just a bit behind. Once that occurs, the earth’s and sun’s gravity would tend to exacerbate the shift away from L3. That’s what it means when we say a Langrange point is unstable. For the stable ones, such as L4 or L5, peterbations tend to be counteracted by the earth’s and sun’s gravity, so the object stays put. Of course there cannot be planets at those points; we would have observed them by now.