The article asserts that major earthquakes cluster around the edges of plates, but doesn't give references.
Yes, major earthquakes cluster in time, but this isn't suprising. Any set of rare events will see clustering in time. It'd be a surprise if it weren't. It doesn't need a cause.
Second, the Christchurch earthquake wasn't anything exception as far as strength, and it wasn't even located on the subduction zone, but another unknown fault 100km inland. What made that earthquake exceptional was that it was very shallow and was directly under the city.
It wasn't even that strong of an earthquake.
The Nisqually quake in Washington state 10 years ago was 0.5 magintudes stronger, but was very deep, which is why it didn't do nearly the damage that it could have, considering it was of the same magnitude of the Loma Prieta quake.
And to predict that the San Andreas is next isn't anything special either. The southern part of the San Andreas is well overdue for a large quake. It could happen tomorrow, but it wouldn't have anything to do with the Chille or Japan quakes.
Third, what geologists are claiming that these quakes are connected anyway? The Newsweek doesn't quote any, and the journalist is not a seismologist.