It's possible because the tonal range of the image is rendered primarily as a range of diffusion of reflectivity. The highly-exposed areas, what we would normally think of as "lighter", are rendered more diffuse through added fine texture, making them somewhat more like paper - the brightness changes in a fairly predictable way depending on the overall lighting.

The less exposed areas, however, retain a more mirror-like finish. If you observe objects made of shiny metal, you'll notice that they can appear dark or bright depending on exactly what they're reflecting to your eye at the moment, which can depend on the angle of viewing, etc.

So, essentially, you have an image where the normally-darker areas can vary in appearace over a huge dynamic range depending on viewing conditions, while the normally-lighter areas vary much less from a "middle" range. This can sometimes result in the "dark" shiny areas appearing lighter than "light" diffuse areas, if they are reflecting a light source towards your eyes, resulting in a "negative" effect.

UPDATE: I took a couple of shots illustrating this, since it's easier to understand visually than to explain:

The difference was created simply by moving the camera a short distance to the right, away from the ambient light source on the left; the exposure was decreased to approximate the eye's adjustment to the change in brightness.

(Original photo is c.1850, and should be well within the public domain in most countries. Any rights to the derivative works are hereby released under CC0).