[idm]

It's called the "file drawer problem" in which research is conducted but not published because it wasn't significant.

You're referring to "Type I error" in which a statistically significant result is obtained by chance, not because the effect is real.

This article does not appear to be an example of the hypothetical scenario you proposed. The trend line is not a "horrid-fit," as attested to by the statistical analysis published in the article - which is open access and may be read for free.

This is a scientific article - and unless you're a scientist, it may be difficult to understand the entire article.