Michael, the PDF you link to in your original post, the link is broken. Can you repost?
Many probiotic foods are acidic...fermented feed, sauerkraut, kimchi, sourdough bread. All of these are loaded with probiotics and one of the byproducts of LABs (lactic acid bacteria) is lactic acid. Sure, the acetic acid in 5% ACV is a stronger acid than the lactic acid in a typical batch of FF, but the ACV is diluted 1:256 rather than undiluted FF. Surely the acid in the FF must be stronger than the diluted ACV...
Also, I have started many a batch of sauerkraut using a tablespoon of vinegar (white or ACV) per gallon of chopped cabbage, salt being the only other ingredient. If the antibacterial effect of vinegar really worked, then the kraut would not ferment properly and the LABs would not proliferate. This has not been my experience as the kraut has always turned out great.
In my passion in learning about all things fermented, one thing I have learned is yes there are good and bad bacteria. Or you might call them probiotic bacteria and putrefying bacteria. The putrefying bacteria cannot live in an acidic environment. You want acids (not sure as far as an acidic environment, beyond my knowledge set) in the gut. Acids from vinegars or LABs are a good thing.
I don't use ACV in our bird's water, but I do use a liquid probiotic called EM, maybe you've heard of it. Yes, I do brew it at home, with a purchased bacterial starter. I have used it for my own use for about 18 months now and since we just got chickens, I give them a choice between plain water and the EM water and they always choose the latter. The EM I brew has a pH of about 3.2 and Braggs ACV shows up as 2.9 ( it may actually be lower, 2.9 is the lowest my test strips gauge). I mix the EM in water about 1-2T/gallon.
I'm on the same page as you, I think probiotics in water is superior to vinegar. I just don't think it's because ACV is antibacterial to all bacteria. It will have such an effect on the putrefying bacteria but will actually help the native probiotics thrive.
An interesting note on probiotics (sorry I have no reference at the moment) is that eating or drinking probiotics, at least in humans, are just passing through. Studies have shown that very few of the ingested probiotic bacteria take up residence in the gut. They do help digest food while they are in the gut, but soon exit the body. Apparently the resident probiotic bacteria are highly specialized and not particularly food worthy...they smell like, well, poop. And the only way (so far) to increase your resident bacteria (say that have been completely wiped from heavy duty antibiotic use) is a fecal transplant, which is just what it sounds like. All this research I'm familiar with is from human studies, maybe there are similars for chickens?