Okay, let's go with that - when fully open, say they draw up as much air as there's gas flowing through the pipe. Now remember that air itself is only about 20% oxygen. So the ratio of gas : O2 in the tube is at best 5:1. Now depending on whether you are burning methane or butane or some natural gas mixture that lies in between, you need roughly about 2 to 6 moles of O2 for every mole of gas. So, clearly there's not sufficient oxygen inside the burner tube. It's only when the mixture reaches the top and sees all the additional air that combustion happens.
Some burners, however, let you draw up a lot more air (it depends on the geometry of the intake and flow rates involved), and by doing so you could accidentally burn through the air in the tube and extinguish the flame.