There are many websites that talk in detail about the dispute of vinegar itself (some say it is allowed, because Rasool Allah SAW liked vinegar from an older narration) and by a newer Madani narration near the time of his death, Rasool Allah SAW forbade some Ashab from converting their wine into vinegar (when the Hukum to make Khamar haram came around).
This debate is TOTALLY Irrelevant to the debate about spirit vinegar.
When we talk about any alcoholic beverage that is sold to be consumed, the alcohol in it is ethanol. The process of making both ethanol and alcohol is requires fermentation.
When bacteria ferment they create one of two possibilities, ethanol CH3CH2OH, or acetic acid, CH3COOH. Acetic acid is a more oxidized form of ethanol. Ethanol is what you want if you're making wine, beer, liquor, etc.
When the fermentation process is allowed to continue, it converts the ethanol into into acetic acid is what gives all vinegars their distinct taste, and the simplest of all vinegars would be a ~3% solution of acetic acid. Most vinegars contain additional flavor components. Any acetic acid in an alcoholic drink is considered bad, since it has a very strong flavor. However, some over fermented alcoholic beverage may contain traces of acetic acid.
In spirit vinegar, the fermentation process is stopped before the bacteria have completely converted all the ethanol into acetic acid. Whereas even a small amount of acetic acid in alcoholic beverages would completely ruin the flavor, the small amount of alcohol left over in spirit vinegar enhances the flavor in some people's opinions.
If this definition of spirit vinegar is valid, then this is not a discussion regarding how the vinegar was made as ... by definition vinegar is made through alcohol. However, a distinction between regular and spirit vinegar is a must.