"Applying ideological bias" is not news.
Then, there is no news -- aside from the weather report.
You can apply ideological bias in choosing what to report, but not in the actual reporting. Take my Trump birther example.
Your example is an interesting case study, because it's an example of how biased reporting on both sides was used to promote a desired narrative, and how people picked their side based on which narrative they chose to believe.
If this particular news had been reported without bias, you would have learned that it has a long and interesting history, crossing ideological boundaries. It began among Democrats, although there is a dispute about whether Clinton's campaign was involved. Multiple reporters have said they were fed the rumor by Sid Blumenthal, but he denies it. How a news outlet treated this particular issue says a lot about their political ideology, and most of them didn't even cover it until they felt compelled to defend Clinton.
The case was also litigated in multiple courts with a legion of DoJ lawyers, before Obama authorized the release of his long-form birth certificate. Fuel was also thrown on this fire in 1991 before Obama ever ran for an election, when a promotional booklet by his literary agency said he was born in Kenya. The responsible person has admitted it was her error, not his.
The story would make a decent book, if someone were to make an effort to interview everyone involved and follow the long and byzantine path to the conclusion.
However, it wasn't fake news. And, while almost everyone has an opinion on it, very few know the entire history. And unless you knew the entire history, you probably didn't realize that you only got the part of the story that you wanted to hear, based on the news outlet that you chose.
Once you lose objectivity, it's no longer "news."
And that's what you are missing: unless you are reporting on immutable facts, objectivity is an illusion. I can write a story with 100% true facts, and it would still be wrong because I left out other important facts that contradict my narrative. But, it wouldn't be "fake".
When Facebook, Apple, etc. decide they need to block "fake" news, what they really mean is "censor news we don't agree with". And that should alarm everyone, even if you happen to share their views.