yes it does flow more volume per unit time, however as spool-up correctly stated, your engine can only fit as much air as the combustion chamber volume allows
Bigger turbos produce lower outlet temps because they dont have to work as hard to make a certain amount of boost, cooler air has more molecules in it per unit of volume (denser) and so more air is going into the engine, which is where some of the power gain comes from.
its all volumetric efficiency that is all a turbo does for and engine
http://en.wikipedia.org/wiki/Volumetric_efficiency
http://www.auto-ware.com/combust_bytes/eng_sci.htm
more air molecules mix with more fuel to make a bigger bang you answered your own question with improves the volumetric efficency of the engine
this question is also like asking why does a twin cam produce more power than a single cam, its the same engine same amount of air going in but there is an improved volumetric efficency of the twin cam head thus makeing lots more power
Boost pressure in pounds per square inch (PSI) is a measure of resistance. For example if you have a really restrictive intake system your boost gauge may say 20psi but if you change that intake system to a much better type you may find that you're only running 16psi. In both examples your turbo is boosting the same amount and your engine is intaking the same amount of air but the restriction (boost pressure) is less.
Same goes with the turbo - so forget measuring PSI.
A T3 on say 15psi is moving X amount of air yet a GT42 is moving 5 times X because of better flow, bigger wheels, increased efficiency.
Does it make any sense?