That is really just a symptom of the second problem. Fake news can spread pretty far before it is debunked, but the fake news has to start somewhere. Maybe people get it from some untrustworthy news site, social media, or directly from the mouth of a habitually lying politician, but it almost never originates from a legitimate news source that has the skills, tools, and motivation to better assess the authenticity of the news. If people put less faith in those untrustworthy sources and waited for actual journalism to be done before reacting, fake news would be less of a problem.
I can honestly say I do not know a legitimate news site. For every topic that I have more than surface knowledge on the articles are always, almost with no exception, biased and limited to a single perspective which aligns with cultural expectations.
The exceptions are local news about local events that has no political angle, and occasionally investigative journalism.
The most common method that legitimate news sources use to bias news is by omission, and second by using a misleading context. Neither is strictly a lie, but the result is as much fake news as something fabricated.
Mainstream news is to a degree more problematic when they formulaically follow a narrative and don’t bother checking the assumptions and present misleading or overreprsenting information.
That’s because people are apt to believe those sources and not critically question them.