Why is this important in the context of Agile teams? Because, if your organizational structure mimics what it was when you had a waterfall process in place, it will be very likely that your teams will _act_ like a waterfall organization and, according to Conway's Law, your software will look like it was produced by a waterfall process.
For this reason, it is encouraging to see that some of the teams at our company have taken big steps towards abolishing the old structures and adapting the whole team to the Scrum roles (Team, ScrumMaster, Product Owner, Stakeholders). Only this type of flexibility and embracing the new concepts can really increase our knowledge of how the Agile methods work, and hopefully why they work...
Oh, and by the way: Merry Christmas, Feliz Navidad, Feliz Natal, Joyeaux Nöel, Hyvää Joulua!