Posting this because the summary going around does not say what the paper says, and the difference matters for how people here are using it.
The mechanism is slowed transit plus reduced intake, and that combination determines which interventions work. Less food means less bulk, slower motility means more water reabsorbed, and the result is a smaller, drier, slower stool. Insoluble fiber adds bulk to a system that is already moving slowly, which is why it frequently makes things worse. Soluble fiber holds water and is the better first choice, and an osmotic agent works with the mechanism rather than against it.
Where I think it is weakest: the comparator does most of the work in how this gets reported, and it is not the comparator most people think they are citing.
The narrow version of the question is what the mechanism is, because if it is transit rather than water then fiber is the wrong lever. Numbers rather than impressions, if you have them.
Note on sourcing:
Figures above are from the primary publication rather than the press summary. If a number here disagrees with one you have, post yours and we will work out which of us is reading a secondary source.