I think Fox News is a good example, because their public messaging has always been "fair and balanced" while at the same time blatantly have a bias; this is just one aspect of how they are clearly deceptive. If instead of calling themselves "fair and balanced" they said they were all about "the Republican Perspective on News" they would immediately be more honest, and it would be easier to understand them as an organization, especially for the people who are regularly deceived by them right now.
I'm not arguing that we should try to exaggerate our biases, or even to center them, but rather, we can become more honest by making our biases clear and explicit to those we're communicating with. Many organizations avoid openly addressing their biases, which makes them less honest overall, and more prone to being deceptive. If you're aware of your biases you can actually account for them, as opposed to letting them blind you. Further, if you're public with that awareness, others can account for them as well, and be less likely to be deceived (even accidentally) by your communication.
Too often, bias is ignored. It always exists. If we name it and make it visible, then we can have a chance at reducing its potential for deception.
Respectable journalism calls this an "editorial stance".
The Wall Street Journal has always been openly conservative in their bias that is most on display in editorials while they maintain a high quality, generally center-right news reporting division.
Similarly the Economist describe their stance as "radically centrism", which sounds a little strange but they outline it pretty well and are open about it.
To be fair, my assumption on that line was always that they were saying they're balancing out the overall news world. Still dirty, of course. Regardless, everyone knows how they lean.
What grinds my gears is NPR. Every member drive they explicitly talk about how their coverage is fair and unbiased, which is way more egregious than some tagline. As far as having a bias and not owning up to it, I think they're the worst offenders right now.