That's not what the statement means. You are distorting a plain sentence to suit your bias. A noisy and visually uninteresting correlation could easily be "statistically significant" with enough data points, but scientifically useless. The social sciences are full of them. No useful research finding in those fields has ever relied on statistical significance. The error terms are just too large for practical application.
The useful findings jump off the paper at you, even though the numbers may be too small to meet the formal statistical parameters. I suspect the atmospheric sciences are the same way.
Meteorology has some well-defined mathematical theory which puts it in the physical sciences and deductive proof. Social science, historiography, the part of psychology that is not physiology use statistics to find patterns or make patterns, but since there is no covering theory of general acceptance the methods tend to be inductive and particular. As they say, history does not repeat, although sometimes it rhymes.