Yes well part of the explanation. It's a lot of delta v to take a comet in the Oort cloud and send it all the way to the inner solar system. But yes it does seem that they think it could explain the origin of the scattered disk, of objects that criss cross the Kuiper belt approaching close to Neptune. Then Neptune would take them the rest of the way into the inner solar system.

That is apart from Sedna etc - they are in resonant orbits so held in place by the new planet X if the theory is right.

This is a link to the paper here: EVIDENCE FOR A DISTANT GIANT PLANET IN THE SOLAR SYSTEM, see their section 5. Scattered disk.

This is a population of large objects that criss-cross the kepler belt in very elliptical orbits and at their closest reach in to just beyond Neptune.

Similarly I think it would be just about impossible for Earth to send an asteroid in to the inner solar system inside of Mercury - not in one go certainly and hard to do it even with many flybys.

But it could help send an asteroid to Venus, then Venus send it to Mercury and Mercury then could send it into the region between it and the sun, and turn it into a "vulcanoid" if they exist.

So, in the same way it is rather that Planet X would help disturb Kuiper belt objects into sufficiently elliptical orbits so they get within the reach of Neptune. Neptune would then perturb them into orbits that take them within reach of Jupiter and Jupiter then brings them into the inner solar system. At least in the majority of cases, would be like that, if I understand this right.

Still doesn't really explain how they get from the Oort cloud though. Just from the Kuiper belt. For the Oort cloud I think you'd need more planets further out  or it could be passing stars that do it, disturbing the Oort cloud as they pass by.

For more about Planet X see:

• Why This New "Planet X" Is No Threat To Earth :).
• Would New Planet X Clear Its Orbit? - And Any Better Name Than "Planet Nine"?