I believe you'll find the rectilinear "distortion" simply proportionalizes the distance differences between the lens and film/sensor center and edge, to the target distance differences, center to edge. They net out so that the photographed image looks like the target.
Correct, provided that the resulting image is viewed from the correct/proportional distance relative to the size, there will be no projection distortion. So, an object sized 1 x 1 metre, when viewed from the same distance as it was shot, and sized 1 metre square, will have no projection distortion. When sized 50x50 cm, and looked at from 50cm, it will also look distortion free.
I like doing multi-image panoramas. If it's just a couple of shots I'm combining, the setting in the photomerge Photoshop procedure that maintains the rectilinear perspective can work, but for large panoramas, the corner stretching looks ridiculous.
Only because we will be viewing it from too far away, which is typical for such wide angle images if printed relatively small. If we were to look from the correct (uncomfortably) close distance that corresponds to the simulated wide angle lens' focal length, it would look perfectly normal.
Reproduction of 2-dimensional subjects is usually best done with relatively long focal lengths, which will then more likely be viewed from relatively close, thus achieving the opposite effect i.e. somewhat compressed (but one needs to get really close to get that sense of compression). Since longer focal lengths have narrower Fields of View, one may need to stitch, but that only helps resolution and automatic adjustment of geometrical lens distortion.
Projection distortion is just that, caused by a mismatch between the viewpoint and original shooting distance, a case of the wrong perspective.
Cheers,
Bart