In many of the old newspaper articles on pillow making, there are references to newspaper pillows. We here at StrangeAgo did not exactly know how newspapers were being used to fill pillows, or why people would use newspapers in something that is supposed to be soft.
The short article below, found in a newspaper from 1909, explains the how and why.
To Stuff Pillows
A satisfactory way to fill art pillows where one can not afford feathers is this: Fold a newspaper in several thicknesses (say eight or ten) the size of your pillow, then put thick pads of good batting on each side of paper. Stuff pillow with this and it will stand up and be as firm as if stuffed with feathers.
Source: The Morning examiner. (Ogden, Utah), 28 March 1909.