I haven't read the actual research, but as described this has the problem that maybe the IQ differences cause the educational differences. In other words, the researchers find that identical twins reared apart with different levels of education have bigger IQ differences than other identical twins reared apart. But how do we know that's not just selection? Some identical twins are (just randomly) very different in IQ. Those ones get sent to very different schools. Nothing to see.

The article mentions that the researchers gathered data on educational systems, catholic schools etc. so maybe they get round this.