The bag is there to contain the oxygen that is flowing from a central source. The flow rate, however, is slower than the capacity of the bag. It's much like the warning, "package contents may settle during shipping" - the warning is more for people's fears than any practical purpose.
Furthermore, as this link shows, the bag is also there to catch exhaled (aka CO2 rich air) as much as it is to hold new stuff.
Cecil Adams (The Straight Dope) reports similar findings. He states:
Here's the deal. Passenger oxygen masks give you a continuous flow of oxygen (as opposed to oxygen on demand, which only flows when you inhale). The oxygen obviously can't flow into your lungs while you're exhaling, so if there weren't some way to store it temporarily it would have to be vented wastefully. The bag makes this unnecessary. When you start exhaling, your breath plus the incoming O2 flow into the bag. When a certain pressure is reached the bag stops filling and the rest of your exhaled breath, which contains more carbon dioxide, is vented through a port in the mask.
The flight attendants make a point of telling you the bag won't inflate (right away, that is) because of an incident years ago. An airplane lost cabin pressure, the oxygen masks dropped down, and the passengers put them on--but when they noticed the bags didn't inflate, they figured the masks weren't working and took them off. Bad idea.
So, is it working? Yes. Is it unsettling? To some people. Regardless, it works, even if not in the way some people might expect.