Like objectivity, I feel like being completely independent in journalism is difficult. Even though all people have different opinions, they do overlap, and that's when/how factions and other groups and labels are created.
It is easier for journalists to be independent from other journalism sources that they might be competing with, but there are always other groups that are divided by class, race, gender, ethnicity, and many more categories that could be potentially problematic to join forces with as a journalist. By labeling oneself with a specific group could be harmful to the credibility of a journalist because a journalist aims to be unbiased, but how can they be supporting a particular group while still remaining unbiased? It's tricky. It's also problematic because if you identify yourself in one way you risk the chance of not being accepted by people who lean the other way. Remaining as unbiased, unattached, and independent as possible is less risky.
Overall though, when I think of independence and journalism the first thing that comes to my mind is freelance journalism. I feel like being a freelance worker makes you connected to more sources, yet actually tied down to less. It almost seems like a lacking of responsibility, but not in a bad way. More like in a safer way actually. Here's some further perks to working in freelance journalism:
Here's an example of a campaign that is promoting another big part of independence in journalism: diversity. http://en.rsf.org/russia-independent-journalism-a-combat-08-10-2013,45302.html
The wonderful thing about independence in journalism is how diverse coverage becomes. There are all kinds of different stories and opinions that are less attached, and that is so much more interesting that hearing or reading stories that share the same opinion as a ton of other people. It really just keeps things interesting.