I cannot promise the 100% authority of this site, but the wording seems legit to me. If you do not concede authority to it, I would suggest going directly to a trusted religious source though:
ETA: Sorry about the original short answer, the product of illness I am afraid. I normally would have at least tried to summarize what they said, but I am a little hesitant to do so on a subject I only have 2nd hand knowledge of. This is significant information there, but the jest is similar to my understanding of the rules. Alcohol is used to produce natural vinegar but the alcohol is consumed in the process. Insignificant amounts may remain, but that is not the point of the vinegar and it is not enough to produce an alcohol effect. Additionally, the use of vinegar is not considered an attempt to get around rules, so the use is considered "forgivable" and OK. Where it would cross lines would indeed be for a fortified vinegar which had alcohol added back in, or maybe the use of just a soured wine which had not been allowed to complete the process. I think where the debate goes the other way are with things like using wine to cook which those that want to use it say the alcohol cooks out, while those opposed admit that it does not all cook out and question that attempts to retain the wine flavor is circumventing the rules and looks like a violation even if not.
This is not authoritative at all, but when I had my own farm I had customers who wanted Kosher and Halal products. I did not do it as it would have just involved too many rules for limited return and customers. But, in general, both groups would have accepted minor violations, provided they were not intentional and major. An example given by the Halal customer was he could consume a melon that had gotten old and started to ferment. He could not however add alcohol to it, or intentionally allow it to get old and start to ferment.