The study was on monozygotic twins, which are essentially one person whose embryo was divided in the womb. They are alike because https://www.youtube.com/watch?v=tbPwzII_g6o. Their ancestors had habits and traits that were developed by acknowledging things that were happening to them and reacting to them repeatedly over time to the point that it was second nature.
I don't believe it's "nurture or nature", I believe it's both.
Now, the reason I said to use siblings that weren't monozygotic is because they would have the same ancestors, but you would see that the genetic memories might not be as strong in one area as the other. They might have some similarities, but they would be few and far between -- because the events of their lives shaped them differently. They aren't one person split into two twins. They're two wholly different people.
as for twins being together at young ages having no effec ton eachother, that's categorically false. Twins (as well as normal siblings, though it is rarer) often develop personalized languages in their early youths which only they can understand, some of which persist into advlthood.