That may well be true in general - twin studies are certainly not the end all of distangling genetic and environmental effects. But if you read the studies results, I think the difference in correlation effect size speaks for itself. In general, identical twins correlate with r value of ~0.5 and non-identical twins with <0.1.

The authors interpret the low correlation in non-identical twins as evidence that the traits being studied are weakly (if at all) influenced by environmental factors that non-identical twins are subjected to. They then infer (assert, w/e) that this level of weak environmental influence also extends to the set of environmental factors that identical twins are subjected to. Now, obviously as you point out, there are environmental factors that are more or less unique to identical twins, but I feel that its unlikely (and so did the authors) that these identical twin specific factors contribute significantly the vast difference in correlation between the two classes.