Sacred Haven of Debauchery

No, there isn't 100% proof, but you shouldn't take the words literally.

The title clearly states that a planet has been discovered.
In reality, they showed that the orbits of Sedna and other dwarf planets are not randomly formed in such strange and elongated ways, with a probability of three sigma. Plus, they showed that adding a planet with specific mass parameters (10 Earth masses) and orbit (not very accurate) explains these dwarf planet orbits. That's the gist of it.
This is not proof that the planet exists. It simply means that the planet fits well into the observed picture and explains it. In mathematical terms, the planet is a sufficient condition for the observed picture of orbits, but it is not necessarily a necessary one.