Yes, it happens all the time. There are many news websites that track and correct lies made by public officials.
There are far better news outlets, and I agree that press and media need to exist and be free for the purpose proposed above, I would just argue that in the most popular media, that isn't really what's happening for most of their audience, and I personally am far happier not seeking out mainstream news myself because of how sensationalist and biased most of it is. I'll eat my hotel breakfasts and airport snacks somewhere other than in front of the complimentary TV.