This seems to be the case. It all ties together to nicely not to be. Sixteen years ago, Firenze (I assume that is who the centaur is, from his views and attitudes) told Lilly that "the world would end if she were nice to her sister", based on the same prophecy based on which he tried to kill Harry: One that was similar to the one Trelawney made.

Remember also the twice-repeated wave of prophecies over the world, despite the fact that we are told that disturbances in time are never enough to cause more than a single prophecy. It would make sense that if any prophacy could be of such import, it would be one about the end of the world.