For as long as I can remember I have been shooting flat art on a "Copy Bench" much like the setup in your article. the simplest, cheapest and by far quickest way to set the camera plane exactly parallel to the table surface is a simple small mirror. Place a plain mirror flat on the table directly below the camera and adjust the x and y axis of the camera until the reflection of the camera lens axis is directly in the centre of the viewfinder. Hey presto! perfect alignment!

What a cool application! Now I can see the iPhone as a staple in the construction industry, where carpenters can level up their beams before driving the final nail. Or I can see my dad with an iPhone: doesn't care for the "phone" or "music" aspect, but it's got a hell of a good level!