I don't think that's an accurate summary of the research. One key aspect of their review is that they don't give much weight to (blatantly confounded) correlational studies. Looking at RCTs that "same risk" is tiny and not statistically significant. For example, looking at all-cause mortality, correlational studies find a hazard ratio of .93, while RCTs find a hazard ratio of .99.

They are definitely saying meat is less risky.