Like Mr_Speedy said, the geometric distortion is reduce with greather focal length.
I would underline two related aspects, the sensor field of view and the focal plane curvature.
At 05 mm focal length, the sensor field of view is about 70 deg per 4000 sensor pixels.
At 17 mm focal length, the sensor field of view is about 20 deg per 4000 sensor pixels.
At 44 mm focal length, the sensor field of view is about 05 deg per 4000 sensor pixels.
Concerning the focal plane curvature, you have to imagine that it is an arc of cricle (the focal plane) and the sensor plane is a chord or a tangent to that arc of circle. The sensor plane seams to tangent to the circle since there are few distortion at high mm and lost of focus all over the dng except at his center, and therefore, no apparent pincushion.
From the previous data, the gap between the arc and the tangent is greather with 70 deg sector than with 5 deg sector. (
http://en.wikipedia.org/wiki/Circle)
Here is a comparaison between DNG and JPG. At the top, sample from the top-right corner; at the bottom, sample from the bottom-left; at the center, sample from the horizontal center. At 5 mm, after correcting barrel effect about 80% and scaling up (1.33)^2, dng leaves moustache effect.

P.S.: On the previous photo, I optimize dynamic range to increase contrast
P.S.: I red the wikipedia defs. To have a curved sensor ...
http://en.wikipedia.org/wiki/Petzval_field_curvatureP.S.: for 4000x3000 sensor, diagonal is 5000 pixels and therefore, about 87,5 deg at 5 mm focal length