<<Disclaimer: Verify this information before applying it to your situation.>>

I believe the chemistry lesson was incorrect. A google search suggested
that commercial vinegar production relies on acetobacteria and
aeration.  There is no concern that apple and wine vinegars are safe.
The concern is about white vinegar.

http://www.nowheat.com/fooddb/food/vinegar2.htm

Essentially, distilled vinegar is not distilled acetic acid that is
then added to water.  What really is done commercially is to take pure
ethanol, add it to water, then ferment with acetobacter.  See the above
reference for theoretical maximum gluten content of white vinegar
(which was based on any protein carryover being gluten only) which
shows one would have to consume over 100 liters a day of vinegar (in
reality 1000 liters if your correct for gluten being less than 10% of
the protein in starch, and that assumes that the base was pure wheat in
the initial ethanol production).

Perhaps the chemistry lesson offered a lesson in commercial acetic acid
production.

Stephen Holland

*Please provide references to back up claims of a product being GF or not GF*