I think this would depend on the project and team you are working on. For my internship I had my own project, which was situated in the context of what my team worked on, but otherwise I had full ownership of the project. As the project "lead", I made every decision, from defining the problem space, to scheduling meetings, to running user testing, and everything in between. However, I still received a lot of support and input from others. So while I was mostly working alone on the project, I also had a network of "stakeholders" who helped me in my research and design process, and offered valuable perspectives on my work.