The meta-analysis is of epidemiological data, which shows association, but since there is no intervention, cannot show causation and does not claim to. It does not distinguish an effect of fiber from healthy user bias.
Partly we use mechanistic evidence to separate cause from effect--that's part of why the article goes into detail about, e.g., how soluble fiber binds to bile in the liver. If there's an association between A and B, and a known physiological mechanism where A causes C which causes B, it makes it more likely that ultimately A is the cause of B.
In an N=1 intervention study, I too found fiber to be health supporting, but that wasn't randomized or controlled.
Fiber lowers LDL cholesterol, slows digestion, makes you feel full longer, and helps with regularity, so increasing your fiber intake is probably worth it anyway.