I am a current PhD student in a CS-related field. My advisors had strict requirements for my first project, but now on my second project I have complete freedom. This was my personal choice, my advisors were/are willing to give me projects, but I wanted to learn how to take a research project from idea to finish. Obviously, CS (and my school) is extremely well funded, so this may be unique.
I think CS has pretty different dynamics than most fields for a few reasons. CS is really well positioned when it comes to both funding received and average funding required to do a project. Similarly, the time required for set up of CS work can often be minimized in a way that is not possible for many natural sciences. And culturally people seem less attached to old school academic status - CS has many viable and relevant career paths for someone that wants to exit academia, some of which even allow for fairly easy reentry to a university position.
