Have a look at the attached PDF file. This is from the 2006 repair manual, but the theory of operation applies to your model as well.
As gas enters the tank through the filler pipe, the air trapped in the tank above the fuel starts to get compressed. If the air had no way to escape, the pressure would become high enough to prevent any additional gas flowing down the filler pipe. As soon as the gas nozzle detects fuel rising higher than the end of the nozzle it is designed to shut off the gas flow.
The purge valve shown on the diagram is only open when the engine is running. It allows the gas vapors in the tank to be drawn into the intake manifold and burned. I don't believe it plays a role when refueling.
The small tube that runs alongside the filler pipe is designed to provide the required escape of air. From what I can understand, the tube is not placed in the highest point in the tank, but rather at a lower level which is chosen so that it becomes blocked with fuel as the level reaches nearly full. Once the tube is blocked a few more liters of fuel can be added before the pressure builds and fuel will rise in the filler pipe and shut off the nozzle.
Since the gas cap forms a tight seal on the filler neck, there is no concern that this vent tube will leak fuel vapors into the atmosphere.
I suggest you examine this tube for any kinks that may be restricting air from escaping. Also examine the opening of this tube in the filler neck to see if anything may be blocking it. Perhaps the little flap in the filler neck is covering the opening when you insert the nozzle, or you are positioning the nozzle so that it blocks the opening.
If I understand correctly, the purge valve will open when the engine is running and release some of the pressure trapped in the tank. In theory you should be able to add several more liters of fuel after driving a short distance.