So I googled.
Before I share my findings, let me assure you that my intention is not to advocate for organic vs. non organic chicken management. However, I am trained in the sciences, and I prefer to understand what I'm doing based on more than anecdotal reports and customs. I also believe that science alone can't give me all the answers, especially since science is so poorly understood by the general public, and particularly the media, and it is often poorly done by the scientific community and poorly reported. But I do have a curiosity about these things, and some formal education in evaluating research, and I have a desire to include cost/benefit analysis in my decisions. (That's the bit that keeps me from installing solar panels on my coop.)
I just don't want anyone to take offense at me. I'm trying to learn here.
Interestingly, when I googled "chicken health apple cider vinegar" I got more recipes for cooking chicken using ACV than articles about keeping chickens alive with ACV, so the jury is out on whether vinegar is good or bad for chickens, depending on whether the googler is feeling hungry or not. I even found one article that advocating feeding fresh cooked chicken to cockatiels to increase the protein in their diet. Who knew???
Also, I found a link to my own response to being directed to Google, post number 22 on this thread. Pretty funny.
I only found two research based articles:
http://www2.ca.uky.edu/afspoultry-files/pubs/Natural_remedies.pdf
From the University of Kentucky College of Agriculture, cooperative extension: "Apple cider vinegar is rich in the vitamins, minerals and trace elements found in apples, especially potassium. In chickens it has been shown to lower the pH in the digestive tract which will make an environment less welcoming to pathogens reducing common infections and increasing resistance to disease. Typical inclusion levels are 1/8 1/4 of a teaspoon of apple cider vinegar to every 110 ml of water (or 4.5 - 8.5 teaspoons per gallon). This level of inclusion will also discourage algae growth. It should be given for 2-3 days at a time."
The article does not specify organic vinegar, and the inclusions described in the article would not be removed by filtering, although some of them might be removed by distillation. I only use distilled vinegar for cleaning anyway.
http://www.rd1.com/lifestyle/poultry-articles/apple-cider-vinegar-garlic-and-poultry
This more detailed article referenced and described a study done by the University of Arkansas which documented the affect ACV on increased acidity in the crop and it's projected effectiveness in reducing bacteria load in the crop, along with their recommendations. The mechanism of this effect would also not seem to be affected by whether the ACV was filtered or not, since the effects are all related to pH.
I read some of Dr. Jarvis excerpts; I'd have to read more, and learn more about him and his actual research. Trying to find more on that. He sounds like he's hawking a product. If he's actually done peer reviewed comparative research between different types of vinegar, I'll be very interested. Unfortunately, many of the articles advocating ACV were indeed trying to sell product, and did not give any supporting references for their claims.
Most of the other articles that advocated organic products used only the "It has long been known" argument. For most of the past thousand years only organic products have been available, so it would be true that ACV can be helpful, and I'll probably use it, and it would also seem to be true that unfiltered vinegar would be the kind of ACV most commonly used over the years and known to be effective. What doesn't seem to be researched is the comparison between unaltered vinegar and processed vinegar. I would love to see some controlled studies on this issue. I might try the good old grocery store vinegar because of cost and convenience. Every trip to a different store in a different part of town to find a more elusive product burns more expensive fossil fuel and adds to pollution. The more stuff I need that I can get in one place, the better off the environment is. And shipping charges to Alaska, when I find companies that are willing to ship to Alaska, are often more than the cost of the product, so ordering online is not always a reasonable option.