Independent from what? I hear that rhetoric a lot in France from people who read Mediapart, an "independently funded" newspaper and website. Their slogan is something along the lines of "Only our readers can buy us."
I always found it quite ironic that their readership seems to feel like that guarantees impartiality.
On the subject of media bias, I suggest reading Matthew Gentzkow's work or even just a survey like this one: http://scholar.harvard.edu/files/shleifer/files/shleifer_cor...
TL;DR: Nope, ownership isn't the main factor in media bias.
"As important, Gentzkow and Shapiro [6] show that, after controlling for a newspaper’s audience, the identity of its owner does not affect its slant.1 Two newspapers with the same owner look no more similar in their slant than newspapers with different owners. Ownership regulation in the US and elsewhere is based on the premise a news outlet’s owner determines how it spins the news. Gentzkow and Shapiro produced the first large-scale test of this hypothesis, which showed that, contrary to the conventional wisdom and regulatory stance, demand is much more influential in shaping content than supply as proxied by ownership."