Co2 (produced by fermentation) is denser than air and thus sinks to the bottom to cover your brew in a blanket and protect it.
Headspace doesn't matter in primary, to be honest you want some oxygen in with it at the start, aerobic respiration of yeast colonies breeds the yeast - more yeast = less work for yeast and thus better brew.
Anaerobic respiration (where alcohol is produced) is without oxygen, so by the time the yeast has used up all the oxygen all should be well, nice healthy yeast colony processing the glucose into alcohols.
Or at least that is my understanding of it, could be wrong but that's the way it was explained to me.
After primary though you want as little air contact as is humanly possible, that's when you'll get oxidation issues.