I did a pure mathematics PhD and was given a general area to look at and a problem to solve but that was really just a starting point, I had the flexibility to solve something related so long as it was interesting. The papers I published had my sole authorship; not even my supervisor's name was on them (except in the acknowledgements). I spent much of my time, for several years, in a room on my own with nothing more than a pencil and paper (except occasionally a book). All I did was sit there and think hard. It was glorious, and definitely not slave labour.
Postscript: I did not go into academia. The PhD helped me get (and do) my job afterwards, possibly not as much as if I had worked in industry that whole time, but it was a fulfilling life experience.