They need to strive to be
accurate and
true. Objective implies neutrality, but the facts aren't neutral.
If a politician says that black is white, the headline "Politician: Black is White" is objective, but not accurate or true.
The reporter knows that black is not white, the editor knows that black is not white, heck the typesetter knows that black is not white. The politician obviously knows too--or at least they should. So the headline should read "Politician Lies About Black Being White." That's really what happened.
Once a upon a time, journalism viewed itself as a check against government--an institution dedicated to holding leaders responsible and accountable. Somewhere along the way the concept of "objectivity" turned them into mere stenographers for the powerful.
Journalists must adapt to the reality that information is not scarce anymore. If people want to know what Trump said on Twitter, they can follow him on Twitter! It's free and just as easy as loading up a news website. So news outlets don't need to just repost what Trump said.
They need to do reporting (and write headlines) that provide accurate context and tell their readers the truth about what Trump said.