I don't believe they claim causality either... unless I overlooked something. Their conclusion advocating for public health measures feels over the top!

The paper does explore the possibility of a linkage and attempts to justify why the observed relationship may be more than just a simple association. They even go a step further by presenting arguments against the likelihood of reverse causality. That they need to consider reverse causality and prepare a defense against it is sort of admitting that they are far from proving causality.

Here are some excerpts from the paper that illustrate this:

  A sensitivity analysis excluding cases at the first follow-up was conducted to examine whether the observed association reflects a possible reverse causality."

  Our results, showing the attenuation of the association of ASB with type 2 diabetes after adjustment for body size measures, were consistent with obesity being a confounder of the association."

  In addition, to rule out the likelihood of reverse causality, we interpreted appropriate models and conducted sensitivity analyses, which strengthen the robustness of our findings."

The authors also include three pages of data, though I neither have the time nor the statistical expertise to evaluate it in depth.

What's frustrating is that the paper never explicitly states that causality is NOT established. While they argue against reverse causality, the absence of reverse causality does not, in itself, imply causality. It may still be a case of correlation. So your point is completely valid.