CWE is completely scientifically sound. It follows on directly from kinetic theory, which is a pretty well-established scientific theory. (Short version: Molecules are in continuous motion. Things happen when they collide with one another.)
Different liquids boil at different temperatures. That's the basis of distillation, and nobody questions that. (It's how they separate crude oil into petrol, paraffin, diesel fuel and bitumen. Each level up the tower is at a different temperature, coolest at the bottom, hottest at the top; substances with higher boiling points rise higher up.)
Well, different solids have different solubilities in water. Codeine phosphate and dihydrocodeine tartarate are more soluble in water than paracetamol. Basically, a water molecule has to hit a lump of solid paracetamol much harder to break off a molecule (which then becomes part of the solution) than it would have to hit a lump of codeine / DHC to break off a molecule. Now, temperature is just a measure of the average speed with which the molecules are moving. At room temperature and especially below, very few of the water molecules are moving fast enough to dislodge a paracetamol molecule compared to the number moving fast enough to dislodge a codeine molecule; so the difference in solubility is enough to achieve a reasonably complete separation. At higher temperatures, more paracetamol will be present in the product.
A vacuum pump and Büchner flask would provide an even faster filtration and so ought to yield a purer product (less time for paracetamol to dissolve in the codeine solution), but such items are presently beyond my means.