It is still origami because there is no such thing as purely clean folds. You opinion is based upon a semantic definition rather than a functional one. Paper might look 2 dimensional from a distance, but it is a 3 dimensional material.

Even the simplest origami models create layers of paper where nothing is truly flat. Paper itself has a tendency to flex and buckle at the creases. Many folders learn to adapt to the variance introduced by paper thickness.

What you have labeled as aggressive twists in complex models are not achieved by such a blunt method. They are flaps where numerous folds have converged. Like the accordion folds in a paper fan, there are many layers that add bulk to the appendage. You cannot haphazardly twist this to produce the final rounded shape. The creases concentrated in the area make it more prone to tearing.