For example: researchers have the budget/resources to to a preliminary study. They use the interesting results of this study to secure funding for a larger sample size study.
Btw, a small sample size study isn't useless necessarily. You can refine methodology, with less on the line. You can also (more or less) validly exclude certain conclusions, to avoid wasting resources on a wider study.
The problem is with pop science headlines, like it is in any other journalistic field. I think it's less of a problem though, than many think. Publishing in the popular press needs to be understood as "academics working on X" not "X has been proven."