There are a few topics where I follow the actual science papers very closely, and this is one. Here's the thing: there are nutrition scientists who conduct surveys with thousands of people, there are statisticians who caution what you can conclude from those studies, and there are doctor/scientist combos who work in prevention clinics.
In this case, it's a group of statisticians who fairly legitimately point to the limitations from survey studies. To be really precise, this is exactly what they concluded:
low-certainty evidence was found that a reduction in processed meat intake of 3 servings per week is associated with a very small decrease in risk for all-cause mortality, cardiovascular mortality, stroke, MI, and type 2 diabetes
That could be true. If the average survey respondent is eating meat 2-3 times daily and they cut out three servings a week, can it really make a diff? What food replaces that meat? A white bagel with cream cheese? That could make it worse.
Statisticians and the public look for very big numbers in those surveys, but ironically the data quality goes down as the survey size goes up because less supervision per participant. Participants don't remember what they ate and how much — and they actually want to forget the extra indulgences.
Data from prevention centers is dramatically different. The Cleveland Clinic published the results of 200 heart patients who sought dietary changes under close supervision over surgery. They were all high-risk patients with a history of heart disease. They had to eliminate all animal foods and refined foods like donuts. In 10 years of close monitoring after adopting the program, one of the 200 had a minor stroke, the other 199 showed no signs of heart disease.
There was a massive study in the 70s conducted by Oxford, Cornell and The Chinese Ministry of Health in China, that wasn't survey-based but did produce huge numbers of participants. They took stool, urine and blood samples, measured weights, assayed their food, inspected the garbage and pantries, and published the results. The data was open sourced and was pored over for years by statisticians. It wasn't confounded by people moving and changing diets, or by much variation in genetics.
It showed absolutely positively and dramatically that people who lived in warm inland areas and subsisted predominantly on rice, veggies, fruit, tubers and legumes had far lower cancer rates than people who lived in the cold north and lived off cattle, or people near rivers and oceans who ate a lot of fish.
That was The China Study. Sir Richard Peto of Oxford became a fellow of the Royal Society in 1989 and was knighted in 1999, in part for his role as coauthor of the study. There has never been a study like that since.