Where viscosity enters the route
Not all fibre has the same effect on bile acids. The most relevant fibres are usually soluble and viscous. When they hydrate, they thicken the contents of the small intestine and can hold some bile acids within the gel-like matrix.
If fewer bile acids are reabsorbed, more may leave through stool. The liver then has to make replacement bile acids, and cholesterol is one of the raw materials for that process. This does not mean fibre blocks fat or makes the whole meal disappear. It means the physical environment of digestion changes. For product design, that makes viscosity a real functional property, not just texture language.