Ah but what if the bag itself was beyond the standard Euclidean Geometry and in fact functioned as a non-Euclidean device? And the bag is in fact, not three dimensional like everything else, but was in fact a four dimensional object. And the bag itself is the only real three dimensional object is the bag itself, while the inside is a four dimensional space which hosts the actual stuff.

Imagine the world as 2D existence on a piece of paper, with every citizen as a two dimensional stick figure, and the bag is featured as another drawing. The could move items around the bag, but when placing a thing in it is now off the page of reality yet still within the 2D bag.

Or something like that. Or Hell, it could just be magic and I move my dude slightly more towards magic inclined. Who knows.