The FCC is supposed to answer to Congress. Congress makes the laws that define the scope of FCC responsibilities. The FCC should only listen to the public as it pertains to regulated entities doing something wrong or the FCC not doing its job.
The FCC is an independent agency. Congress defines the scope of it's powers and the president appoints it's chairman and members of the board. However, when exercising those powers within the scope of it's statutory authority the FCC is answerable to no one, not even the president. If the FCC pisses off congress they have the power to redefine the scope of it's statutory authority, but that's about it.
I do agree that the FCC head should never be a shill for the regulated industries.
Agreed. If congress had any backbone they would place ISPs under Title II by statute and take the decision out of the FCC's hands.