It's impossible to write a completely neutral article, in my opinion. There's limited space in a newspaper (or for a blog article, or for a TV news spot, or whatever) so you have to choose what to say, and how to say it.
Say that two people both write an article about a piece of civil rights legislation being passed by Congress. Both people can write an article that is completely factual and accurate, and yet the two articles will likely have significant differences. Different people might be quoted. Different descriptive phrases will be used. One writer might focus on the lengthy debate that preceded the legislation's passage. The other might choose to focus on the legislation's effects. And so on, and so forth. And without even intending to do so, one writer might come up with an article that seems more sympathetic to the Democrats, and the other might seem more sympathetic to the Republicans.
This is unavoidable; but what is avoidable is writing an article that slants one way or the other on purpose. If you analyze a particular news organization's articles in the way that the researchers in the article did, and you find that the majority of bias is going in one direction, I think that's a problem. It's not possible to avoid all bias, but it is possible to attempt to write articles that are as factual and neutral as possible, and I believe that if you do that, you're not going to skew too far to one side or the other.
I also think that as a more practical matter, having an editorial staff that reviews and corrects articles before sending them out is critical, because then you've got two sets of eyes, minimum, on all of your material. But as news budgets are being slashed everywhere, particularly for newspapers, editorial oversight is going by the wayside. Most publications don't even appear to employ proofreaders these days.