If the student wishes to be self-sufficient in PhD research, then she/he ought to express that the student is competent to do so.
There are supervisors who tend to give sufficient freedom for the student to do their research in their own accord. There are some others who feel much more procedural in their approach to build and shape their scholars to their view. Both are actually fine as long as they confirm to the type of their respective students. There are some who require more attention that others, and some others less so. If the student feels that she/he does not require to be spoon fed, then it would be up to the student to show that she/he is capable of producing valuable result by him/herself.
The student ought to exhibit active involvement in the research and request for suggestions to the advisor. Here are a few examples.
There is this new problem I've just came across while doing this work. It's about .... May I look further into this?
There is an idea I would like to discuss regarding .... Shall I try this one out?
The point is to show how eager you are to be able to do research with lesser support. Of course this might not work all the time (depending on your advisor). This would, however, show how capable you are and is certainly worth a try.