It is, that's how it works. Relative to the planet the incoming and leaving speeds are the same, but during the flyby the trajectory relative to the planet's orbital motion changes. So if you come in from the "side" of the orbit and leave headed in the same direction as the orbit, you'll increase your velocity relative to the Solar System by the speed of the planet. But that's the most you can gain from that.
Jupiter is the best planet for orbital slingshots not because it's going the fastest, it isn't, but because it's high gravity makes it easy to "bend" the trajectories of spacecraft a lot, so you can gain a bigger percentage of the orbital speed easier, which makes for a higher total speed.
Notice how extreme the changes in direction are for the passes by Jupiter and Saturn, versus Uranus and Neptune. They are very sharp curves, that go from nearly approaching the planets from the side to leaving nearly in the same direction as the planets are moving. You can pick up at most 43% of Earth's orbital speed from a single gravity assist at Jupiter, but that's still a significant amount.
Additionally, as you can see from the second link, the farther out you are from Earth (at least in the more inner parts of the Solar System) the more bang for the buck you get from speed increases, because you're higher up out of the depths of the gravity well.
He's correct. Remember how much further out planet 9 would be from the sun than Jupiter is. The speed at which an object orbits is related to how far away it is - note that the article said it has a really long year, too. Consider how far away geostationary satelites are compared to the ISS. The ISS goes around the planet several times a day, but geostationary orbits by definition complete one orbit in one day.
