The problem with a lot of ferment-on-premise owners and home winemakers (and don't anybody get offended as I have worked at an FOP for a considerable amount of time and am a home winemaker!!) is that their wine literacy is not always all that great.
What I mean by that is that there are plenty of FOP's in business that are turning out oxidized, flat crap to their customers and because neither know any better, everyone is happy with the result. My parents are like that... they make wine at a FOP and the stuff is garbage, but because it's cheap and easy and they don't drink much else, they're happy with it. I occasionally make them some "good" wine but they are still pleased to buy their cheapo plonk because they tell me "we can't really tell the difference." PLEASE!!!?? Can you not tell the difference between processed cheese slices and a good chunk of aged cheddar? Same deal... Anyways, that's enough ranting about my parents, but my point is that you have to take people's winemaking advice with a bit of caution... just because they are satisfied with their process doesn't mean that it is the best possible practice.
Same goes with a fair amount of home winemakers... they drink what they make and nothing else, so they are none the wiser when it comes to flaws or shortcomings in their wine.
Sure, if you don't take off the airlock at all after adding stabilizers and fining agents, there is probably enough CO2 gassing off of the wine to form a bit of a blanket on the wine and avoid any serious problems with oxidation, and your wine will probably be alright for awhile. BUT, minor oxidation can result in a loss of aromatics which might not even be noticeable as a fault but it is robbing your wine from being as good as it possibly could be.
So while I'm sure you can get away with some headspace for a considerable time without developing major faults, don't fool yourself into thinking that there will be no adverse results in the wine.