This is a slippery concept. The straight answer to the question “Can printing ever match the color of a painting exactly?” is a simple “No”. The trouble is not so much the “match exactly” as “the color of the painting”. Because of the way vision works the same painting will look different in different lighting conditions. If there’s any daylight involved, it’ll look different under different weather conditions and at different times of the day. This is because the color is not inherent in the object; it’s a consequence of the reflected light hitting your eye. So there’s no “exact color” of anything that you might try to match. The best printing can do is pick one state and match that: and using the little dots of the halftone process* it can do that amazingly well.
Here are four pictures of the right hand panel of the Portinari Altarpiece, by Hugo van der Goes.
These are of course digitized photographs which adds another layer of distortion. Well actually the first three are photos and the fourth is a photo of a Giclée** print.
The first one has a sky which looks like a storm is brewing while the others all make it look like we are enjoying a nice sunny day (except the third where the blue sky has been cropped off, though, in compensation almost, that band of white just above the horizon has become a sickly light blue.) The background landscape in the second one is notably brighter than the others. The red of the dresses is different in each one of them and the Giclée print reveals that the little kneeling figure on the right is wearing a green dress, not a black one like her big sister. The standing figure on the right either has a white dress or a yellow one, though the print kind of goes for beige.
So what’s a pressman to do? The best a printer can do is to match the original copy supplied by the publisher. Nobody gets to fly off to Florence while the job’s on press. Who knows which of these pictures best represents the original. If you go to the Uffizi, it’ll depend on the lighting which of the originals you’ll pick, and someone else who goes on another day will no doubt see something slightly different.
MORAL: make sure your author provides good photos, ideally all taken under similar lighting conditions, then proof carefully in order to have your halftone reproduction match the original photo, again under controlled lighting conditions. You’ll end up having to trust your author, ‘cos you’re not going to get to fly off to Florence either to see if the originals really do match the painting.
See also Color matching
* This picture illustrates halftone dots rather well. See also Screens and screen finders.
** Giclée is a neologism coined in 1991 by printmaker Jack Duganne for fine art digital prints made on inkjet printers, as Wikipedia tells us.