I believe they were a replacement for Only-On-Terrain, a setting that was used in the DOS/Lemmix days which caused an object to be shown if and only if it is overlapping terrain (pixel-by-pixel). This setting could be applied to any object. But in practice, it was almost exclusively used for one-way-walls.
A few levels in the original game use it for decoration, but it's not many (and not in the DOS version). I can think of two off the top of my head, namely Fun 20 (We are now at LEMCON ONE) and Mayhem 7 (Poles Apart) (they use the same layout). I'd have to play through the Amiga version again to see if there's any others that use it, but this particular instance can be replicated using resizable water objects. In the DOS version, the setting does not render properly (specifically, the colors get messed up) when used on arbitrary objects, but it's hard to say if this is a bug or not -- the DOS version culls a lot of decorative terrain/objects anyway, and thus it's possible that they only considered one way wall objects when they designed the DOS implementation (perhaps they could make it perform better that way).
If I remember correctly, the Paint setting was a designation for decorative objects that are intended to be used with the Only-On-Terrain tag, with the intent being that those objects would become paint objects and then Only-On-Terrain would be culled. OWW in NL have had the behavior for a while out of the box with no need for the tag, and on other functional objects the Only-On-Terrain tag would probably be considered a bit of a troll to make use of it.
