Some background info for non-chemists: dioxins are members of a specific group of chlorinated cyclic organic compounds. These compounds are formed when certain organic compounds react with chlorine. These organic compounds aren't something from Whole Foods, but rings of carbon and hydrogen, in this case also having chlorine atoms attached. Dioxins are formed during garbage incineration, and as by-products from assorted industrial reactions involving chlorine. Ok, end of nerdy part.
As part of my work involves book and paper conservation, I've studied up a little on paper production through the ages. Old paper was made mostly from cloth rags, and was naturally white and strong, and was not bleached other than maybe being laid out in the sun to whiten. Our parrots would have been perfectly safe with that paper.
As demand for paper grew, it outpaced the supply of rags. People learned to make paper from wood fiber. The wood is ground up and soaked, then beaten with mechanical beaters to separate it into fibers. The fibers are washed and made into paper. Wood contains lignin, which doesn't wash out of the fibers at this early stage of processing. The wood pulp fibers, containing lignin, are used to make newsprint and the inner part of corrugated boxes. Lignin weakens paper and causes it to darken over time so it's not good for high end uses but works fine for newsprint and for the inside of cardboard - that kind of paper doesn't have to be white or strong.
Takeaway: newsprint itself is very safe in terms of dioxin content.
The next steps are usually called the Kraft process and involve treating the pulp with bleach and other chemicals to whiten it, remove the lignin, and other complicated things to make the pale white and strong. Depending on the use, paper might get a clay coating to make a smooth surface for glossy printing, sizing for rigidity and strength, etc. and all papers made from this treated, whitened pulp will contain some level of dioxin. Every EPA and other study I've seen says these levels are safe.
Things that use LOTS of this white paper pulp include paper towels, diapers, and sanitary pads.
The dioxin is generall not a hazard unless it gets into the body. There are two ways this can happen. It might dissolve in water, like when you wipe up spilled water with a paper towel. But it isn't in contact with your hand long enough to get through your skin, usually. Wait, what about liquid that stays in contact with the body, like pee in a diaper? Good question. Manufacturers have taken great strides to reduce contaminant levels for these uses, and it might be true because I don't see Pampers getting sued up the yin yang.
The other way you can pick them up is by skin contact, usually some oil on the skin. The oil or water needs to penetrate the paper, dissolve the dioxins, then carry them through the skin. This is considered a fairly low risk.
My interpretation of all this is that newsprint is very safe for parrots to chew. As paper moves up the whiteness/strength scale it picks up traces of dioxin. This includes that brown kraft paper - the stuff in rolls and on the outside of corrugated paper - as well as white printer paper and the like. My opinion is that this paper is also pretty safe for parrots as long as they aren't ingesting it. Paper in water bowl is most likely to be bad, paper eaten by birds can leach chemicals into the bird. Most parrots have dry tongues and dry feathers so probably don't pick up much, if any, dioxins from paper. This is my fairly educated opinion and I haven't done any personal tests with a mass spectrometer, and I think the official government studies saying levels of dioxin in paper are safe are likely correct.
Synopsis: don't let your parrot dunk paper in his water dish, eat paper, or sit on wet paper. Plain newsprint is safest and hardly any risk at all. Brown kraft paper isn't much different from white paper, and both are reasonably safe for parrots to rip up as long as they don't eat it. Chemicals such as chromium in ink - that's another story.
