Deez, there is a term for this: confirmation biasSuperb points all the way around. I think you draw the line well. I've heard that there is a conflict in journalism circles about whether a journalist's job is to report both sides of an issue or political race and let the public decide or whether it's to report the "truth" (as the journalist sees it). In the literal sense, I think a journalist should report the truth and call BS on a candidate who tells a falsehood. He or she shouldn't allow something that is factually false to go unchallenged.
However, there are two problems with this mindset in the context of political reporting. First, the modern media doesn't know what a "fact" is anymore. They will deem certain things to be facts that are actually opinions that are simply unquestioned by political elites or just unverifiable. Politifact (or Politifiction as I sometimes call them) is notorious for this.
Second, the media usually applies a double standard in how they report the "truth" and how they characterize a falsehood when they do call one. Hillary wasn't held to anywhere near as high of a standard for honesty as Trump was. Furthermore, when she was caught in a falsehood, it was usually framed as a "misstatement," an "inaccuracy," or an "inconsistency." What term was usually used to describe Trump's alleged false statements? They were routinely called the far more judgmental "lies."