Undried pine has phenols in it--that's what make it smell like pine. You may notice that kiln dried pine doesn't smell very "piney" because these compounds have been baked out. Phenols can irritate mucous membranes, which is a big deal for bunnies whose sensitive noses are going 24/7. Rabbits also have sensitive eyes.
As indicated in that article (sorry I don't have time to read all of it, but just skimmed it), these compounds induce some enzymes in the liver. This means that they cause these proteins to be over-active and thus break down things more quickly. Therefore, an animal on pine bedding will metabolize a drug more quickly than one that isn't, and this can cause problems both in determining the right dose of a drug to give, and in the way the animal gets some nutrition from food. Not only drugs are metabolized by these enzymes, some compounds in food, such as vitamins, are. This means that a rabbit might not get as many vitamins as they should.
Also, breaking down drugs and other things more quickly can make the byproducts of these compounds be more concentrated in the body at a given time point, which could be problematic. For instance, if vitamin X is degraded to compound C that is more toxic than vitamin X, the concentration of compound C increases. If compound C was previously produced slowly enough that the body could get rid of it (usually in urine), this increase in its concentration might overshoot the body's ability to eliminate it, and levels could build up to be toxic or dangerous.
Finally, induction of liver enzymes puts stress on the liver, and that's the last thing we need with rabbits. They can be prone to fatty liver disease, and the liver is a very important organ in the body that we really need to protect. These same enzymes are induced in humans when they are chronic alcoholics, so keeping rabbits on phenol-producing bedding may cause liver damage akin to chronic alcoholism.
I think the respiratory issues alone are enough to keep small animals off of pine and cedar bedding. The liver issues are a bit controversial, but there is just too much evidence that they could be a problem. I know the lab animals I have seen (from mice to rabbits and on up the evolutionary tree) are not kept on pine bedding. Perhaps that is because I have seen animals involved in pharmaceutical testing, and they don't want the livers of these animals to be at all influenced by their bedding as the metabolism of a drug is primarily what they study in that kind of test.
Kiln-dried pine pellets (like Feline Pine or wood stove pellets) are cheap and becoming more readily available. They're the best solution for bunnies' health and the wallet.
