First of all, I think this is a great method. I really like the fact that you push down as if it were being sprayed, to let the needle pass down, and the liquid pass up. I was wondering how one could do that without damage to the sprayer mechanism. More than nice - it's a real hack!
The closest thing I have seen to this are those scent genies, which basically allow for direct passage of liquid into the decanting vessel, by virtue of having what amounts to a sprayer-receiver on the bottom. In non-fragrance, some spray oils (like Rem-Oil) have thin plastic tubes that fit into the spray-head, in order to deliver a stream, but frankly that's a bit crude next to this.
Before I weigh in as a chemist, I'll offer a comment as a physicist or a physical chemist. The law of conservation of mass (we don't need to worry about energy, unless this is Eau de Chernobyl) basically says that if you smell anything, you're losing something. The question is really whether there is a change in composition in what remains liquid. The intuitive, gut answer is correct for compositions like fragrances. The vapors will have a different composition from the liquid they left behind. More volatile stuff will escape faster. Vapors *must* be richer in topnotes, and liquid MUST be richer in basenotes.
Is the differential enough to worry about? No simple answer. I tend to spray-decant very quickly, carefully, and forming as much of a "closed system" as possible, by using a small funnel, by streaming when possible, by spraying quickly and efficiently when it's not. I feel that there is very little change in composition. But the bottom line is that Brian's method is going to reduce topnote loss and oxygen exposure to almost as low as they can possibly go. If you want to remove all doubt, use the syringe method.
A simple fact from the organic chemistry lab proves that this method is superior. When removing chilled, pyrophoric (instantly burn or ignite in air) liquids from their septum-sealed, refrigerated bottles, using syringes with long needles (which incidentally is a very dangerous operation, which killed a beautiful female student rather recently due to - if I remember correctly - a plunger separation from the syringe), it is instantly apparent that air contact with the fragrance pyrophoric liquid is taking place, because the liquid will smoke, smolder, or burn brightly as air contacts dripping liquid at the end of the needle, depending upon the degree of pyrophoricity. Were one to spray liquid from the end of the syringe, the reaction would be colorful at the least, and highly dangerous even more likely. Thus, one sees why for the more pyrophoric substances, performing this operation in a glove box under an inert gas like nitrogen or argon is preferable, if not mandatory.
In any case, there is no doubt that contact with oxygen and evaporation occur when liquids are exposed to air, and that spraying produces immediate and intimate exposure to oxygen. That contact isn't the end of the world for a fragrance, but every oxygen contact and every spray nickels and dimes it, just a tad, IMO. I'm sure you could measure it with machines. No doubt about it. But is it enough to worry about? Most cases, for a single decant, probably not. But I'll bet that there is a xerox effect with decants of decants.
I think it's clear that Brian's method is as good as it gets, short of decanting with a syringe in a glove box under argon.
I am curious if this method can be applied to even the most stingy and inaccessible spray-head, by using a thin enough needle, applied into the tiny outer hole of the spray-head, in its depressed state. Very cool if so.
As for injecting small amounts of air into the bottle before withdrawing liquid - I don't think it matters, since air will ultimately seep in to equalize the pressure at some point anyway. One could inject nitrogen or argon to be totally lab-grade about things, but I think that a bit of air is not much different from what would happen anyway with normal use.
I'll be looking into syringes for decanting my most volatile citrus fragrances, for sure. It's easy - so why not? I use a syringe for filling motorcycle batteries, and I care a lot more about my frags.
One last thing - people around here do have good noses. Raise your hand if you have a bright citrus frag that has gone flat after a couple of years. You know what I'm saying. Evaporation of topnotes is quite real.