So this guy is actually misrepresenting what the paper says. It says "Weak but Significant". Meaning that there is a definite correlation. 

Here are the results from the author. 

"We conservatively estimated that—relative to zero consumption—consuming processed meat (at 0.6–57 g d⁻¹) was associated with at least an 11% average increase in type 2 diabetes risk and a 7% (at 0.78–55 g d⁻¹) increase in colorectal cancer risk. SSB intake (at 1.5–390 g d⁻¹) was associated with at least an 8% average increase in type 2 diabetes risk and a 2% (at 0–365 g d⁻¹) increase in IHD risk. TFA consumption (at 0.25–2.56% of daily energy intake) was associated with at least a 3% average increase in IHD risk. These associations each received two-star ratings reflecting weak relationships or inconsistent input evidence, highlighting both the need for further research and—given the high burden of these chronic diseases—the merit of continuing to recommend limiting consumption of these foods."

Along with a link to the actual paper