Most commonly this fear is impressed on brewers when talking about brewing a beer in a fermenter much larger than the volume of beer going in. This seems mostly myth/misinformation than possessing any real basis. My experience certainly suggests the headspace issue is overblown. Look, most of us began fermenting five gallons in eight gallon buckets. That's three gallons worth of headspace plus the oxygen permeability of the HDPE. How many people find their buckets full of vinegar?
I've fermented lots of undersized beers in a 7.9 gallon bucket. I've fermented three gallon batches and left them for up to three months without a hint of vinegar. I've brewed one gallon batches in that bucket. I have one going right now. It's actually a second beer brewed on the cake of a prior one gallon batch. I intend on brewing two more one gallon batches on it before I clean it out. It's been in use, full of beer, since the beginning of March. It will probably get emptied and refilled in a few days and then emptied and refilled in early June, so it will go a full four months. I don't expect to taste any vinegar at all. My lambic solera sat for a year -- at one point I had to take the cap off and move it -- then was partially drained and refilled. No vinegar.
I even have some diluted wine I'm trying to turn into vinegar that's been sitting exposed for about a month. It's not even vinegary. Now some fruit flies did take a swim in it (and died) this week and it is starting to smell a little vinegary. So clearly oxygen exposure itself is not enough.
Make no mistake, I'm not suggesting beer never turns to vinegar, but if your beer is turning to vinegar, you probably have an infection issue/sanitation issue that could be addressed.