It shows there is zero correlation.
For example, imagine we find that higher speed limits increase the rate of automobile accidents in a given area. That finding doesn't preclude that poorly maintained roads might also increase the rate of accidents. So just the existence of an area with a high level of car accidents and very low speed limits doesn't necessarily mean that there is no correlation or causal link between speed limits and automobile accidents. It may just mean that the area suffers greatly from other causes (like poorly maintained roads).
Similarly, I think it is fairly intuitive to assume that there are probably a host of causal factors in suicide rates. For sure, means isn't the only factor but it is an important one.
There's been research into means reduction, and it does seem to have an effect on reducing suicide. The hypothesis is fairly intuitive: many suicides are a response to a crisis, and a human in crisis-mode is not always a great problem solver; lack of an obvious means sometimes gives people some extra time to reconsider.
You can read a high level summary of some of the research here: https://www.hsph.harvard.edu/means-matter/means-matter/risk/