Is the takeaway here that a strong correlation between the absence of a certain factor and the absence of another factor in a representative sample provides evidence that a causal relationship exists?

I understand that one way to weaken a causal argument is by providing examples of an effect in the absence of an alleged cause (or vice versa). In the same vein, is it safe to say that you can strengthen a causal argument by showing there's a strong correlation between the ABSENCE of an effect and the absence of a cause? In other words, in a large, representative sample, can we say that: no cause + no effect = a causal relationship exists? (Sorry for using caps! Not meant aggressively, just for emphasis and I can't italicize here)