Is it true that shotguns' relative short range is actually BS?
Largely. The pattern of shotgun pellets spreads approximately 1" for each yard it patterns—or, if you prefer, approximately 3cm for each meter. With the larger "buckshot" type pellets, each pellet is about the size of a pistol bullet and they have to be stacked inside the shell in a certain pattern or else they won't all fit. From a shotgun, buckshot is lethal out to 40m+ and can be used for suppressive fire out past 100m.
There is also "slug" ammunition, which contains one large individual bullet instead of many pellets. A highly skilled user can get over 200m effective range against man-sized targets from slugs, though hunters generally prefer to stay inside 75m with them.
On the other hand, a highly skilled user using a centerfire rifle and a telescopic sight can go out past 600m, maybe past 800m, depending on his skill. Shotguns have less effective range than rifles, but not many hunters try to sling lead at deer from 600m. And in combat over 90% of rifle fire takes place within 200m, well under 100m in urban or jungle environments.