Is it actually possible to draw the correct perspective using only affine transformations? I thought that was the point of the article.
It is possible to approximate perspective using piecewise affine transformations. It is certainly possible to match the perspective transformation at the vertices of the subdivisions, and only be somewhat off within.
With 6 degrees of freedom, you can only fit 3 2d points at a time. Triangulation causes the errors shown in the article, hence why subdivision is needed.
I think GP's point is that besides the unavoidable distortions coming from approximating a perspective transform by a piece-wise affine transform, the implementation remains incorrect.