Fibers do interfere with the absorption of nutrients, as Plornive stated. One mechanism is by physical interference, such as with soluble fibers, which turn into a gel-like mass in the intestines. This gelatinous mass will physically hinder the movement of nutrients to the intestinal wall (where absorption takes place) and also slow the movement of enzymes into the mass, thus interfering with digestion (things not digested properly are not absorbed properly).
Another mechanism is by decreased transit time. Bulking agents speed up the movement of nutrients though the intestines. If the mass moves through faster, then there is less time for proper digestion.
While fiber can reduce some food absorption, it is not a major reduction, probably no more than 10% max.