there's probably something to this. but, correlation coefficients work as follows.

1 - completely positively correlated; if x then y.
0 - no correlation at all.
-1 - completely negatively correlated; if x then not y.

anything between 0 and 0.5 is pretty weak. 0.09, 0.13? that's evidence of almost no correlation, suggesting almost no relationship. the math suggests the opposite of what the article is saying.

https://www.motherjones.com/environment/2013/10/vaccine-denial-conspiracy-theories-gmos-climate/