Good faith is required to accept any type of reporting. Otherwise, your question can always be extended to "How do we know that they didn't just make it all up?"
The researchers did not report conducting more comparisons and they did not adjust for this in their analysis, so we have to assume that they are telling the truth.
Of course, there's always the chance that they are being deceitful, so we have to reserve some skepticism and take into consideration related studies before forming any firm conclusions.
In this particular case, the correlations that they found have quite strong effect sizes with p < .001. Figures 2 and 3 are quite striking. These results are also supported by previous research. That doesn't mean the matter is settled by any means. It's just another piece in the puzzle. But there is no indication whatsoever that they are p-hacking or going on a fishing expedition.