Yes. A recent twin incident proved that nurture plays a surprisingly large role, larger than was expected by the investigators.
It actually tries (weakly) to claim the opposite, with statements like "Carlos and Wilber both had very similar white mobile phones" and "We are a little bit more ego-centric, bigger flirts."
Nothing about nurture playing a role though.
Project about them: http://drnancysegaltwins.org/bogota-twins-project-gallery
The best reference I can currently come up with is this comment by tokenadult who has a longstanding interest in twin studies: