Causality means that the 2013 box being bigger makes the 2014 box bigger. If they are independent, there are many priors where making the 2013 box bigger makes the 2014 box bigger.

Katja's argument is that SIA makes the "human-like civilization" box bigger. But observations say that the "colonise the universe" box isn't big. Hence we can conclude that the causality breaks down between the two boxes - that human-like civilizations don't tend to colonise the universe.

The argument is a bit more dependent on your choice of priors (see http://lesswrong.com/lw/1zj/sia_wont_doom_you/ ) but that's the gist of it.