I'm done screwing around, the below is meant to be serious.
The origin point of most sprites is not the bottom of the sprite, it's typically a few pixels above. I've created this crappy little image to demonstrate what I mean:
The green dot in the middle of that cross on the bottom plane of the box is the origin point. You must remember, Doom's sprites were 3D models (of clay, not polygons, but still 3d and still models nonetheless), they were not flat. If they were flat, and did not have depth, then it would be safe to assume that the bottom is the origin point.
And again, they are drawn below. Their origin points are in the negatives vertically, are they not? And yes, you would see them if they were below the ground, since the Doom engine does not clip sprites against flats.
The offset is below the origin point, therefore, it is below the ground. Visually, they are not meant to look like that, but the fact is that the sprites are below the ground.
They are not drawn right on the floor, if they were, they'd look like they were floating a few inches above the ground. They are offset below the ground to correct this, so that the bottom center of the actor is at the origin point, and not slightly above.
As for those images, the first one is of course how it appears in game, but the second image shows what they are physically supposed to be, size wise.
These sprites have depth, the front of what space they take up is closer to the camera than the origin point. Things that are closer to you look larger. Therefore, the sprites are slightly larger visually than they are physically, to account for the fact that the front of the sprites space is not at the origin.
The main problem with how you are interpreting this is that you are interpreting it as strictly 2D, which it is not. It is 3d space being rendered on a 2d surface.