One could say we value the scientific method in policy discussions, but that may be a hard sell when looking at some of the counterexamples, with the WMD fiasco being a particularly pointed one.
In that example, the media was involved in giving the government position the credibility it needed. For example in now famous articles: Gordon & Miller, NYT 2002-09-08 and Gordon & Miller, NYT 2002-09-13. Scientific inquiry in real-time was not possible, however.
A better defense of the integrity of discourse, is that the high priority given to freedom of speech would allow public criticisms of the conventional wisdom at any given time. In the long run, if more factually correct narratives are available, they would become accepted. This is one of the most prized principles in the modern world.
On the side of the skeptics are theories such as in Manufacturing Consent, which argue it's possible to subvert the mechanisms of public inquiry, and that this is actually commonplace in specific but important cases, like when national security or large sums of money are at stake.
In this case, there are parallels visible in the media. In a twist sure to tweak some readers, one of the prominent newspaper articles promoting the turnaround on the Wuhan Lab Leak news story, was co-authored by possibly the same Michael Gordon who also co-authored the 2002 WMD articles in the Times mentioned above. This time writing in the Wall Street Journal: Gordon, Strobel, Hinshaw, WSJ 2021-05-23.
However, in my opinion, it's too soon to judge, and it's too heated a topic to expect perfection in reporting. To expand on one of the more frighteningly candid quotes of the Bush administration- due to lack of full information, the only position one can take is that it will one day be a matter for future historians.
Journalists don't really have a choice, and in practice have extremely strong incentives to report the officially supported position in their locality, when there is a political consensus.
So to actually answer the question, what Keeps the Press Honest? In the above I am implying that in some potentially very important situations, it is not any of the following:
- The scientific method, when events happen on too fast of a timescale compared to the work of science
- The media industry itself, when it faces pressures to conform
- Governments or political groups, when they are subjects involved in the stories being reported
I'd suggest, by process of elimination, that the answer is you.