A lot of the details of a proper bedding job have been learned by trial and error, and passed around. Often, we know that a thing works, and have a theory about why, proof is harder to come by.
One of the main components of accuracy is consistency, from shot to shot. Without some form of bedding, the barreled action will shift around minutely from shot to shot, resulting in inconsistent vibration patterns.
Pillars are there for two reasons, first to keep the bedding from being distorted by the action screws being tightened, and also to allow higher screw settings, which may be beneficial to accuracy. Without pillars, depending on the material that the stock is made of, action screws may only be tightened to about half (or less) of the torque that is usable with pillars. This is particularly important for actions that have minimal bedding area, to create sufficient friction between action and stock for a stable joint.
As to the matter of action screw contact, I can tell you from repeated personal experience that this is the case. The answer as to why could become over long for this format. I have fixed more than one bedding job for a friend by simply opening the screw holes in the stock to eliminate contact. The difference in accuracy has always been quite evident.
