Ugh. Every time one of these stories comes up, someone has to bring up Velikovsky. As someone who studies early solar system evolution, I've had the "pleasure" of talking with Velikovsky supporters on numerous occasions. What Velikovsky wrote about was wide-scale rearrangements of the architecture solar system WITHIN HISTORICAL TIMES, based on nutty interpretations of classical mythology. What the article here discusses is a hypothesis for the formation of Triton during an event called the Nice model that is thought to have happened about 3.9 billion years ago (based on dating of large lunar basins from Apollo samples). During this time, a much more massive precursor to the Kuiper belt fueled the migration of the outer four giant planets, disrupting stable reservoirs of small bodies throughout the solar system. Once the ancient Kuiper belt was depleted of mass, the migration stopped (so the "fuel" is gone, and therefore this process can only occur once in the lifetime of the solar system). Had planetary migration occurred within historical times, then we would currently be in the midst of a massive bombardment of comets and asteroids, and the Earth's oceans would currently reside in the atmosphere (along with perhaps some rock vapor clouds).
The Nice model and Late Heavy Bombardment is backed up by observations of the structure of the Kuiper belt, observations of other solar systems around other stars, radioisotope dating of lunar rocks (in a variety of isotope systems, but most especially K-Ar, and U-Pb), observations of the structure of the asteroid belt, dynamical models based on plausible initial conditions for the early solar system (constrained by aforementioned observations), observations of zircon crystals found in ancient Earth rocks, cratering chronologies of the rocky planets, the Moon, and icy satellites. Basically it's a preponderance of evidence pointing toward plausible models for the early history of the solar system. Velikovsky has tortured interpretations of ancient literature. Who do you think is more likely to be closer to describing reality?