I don't know if all their arguments hold any water, but I can tell you that it does save a significant amount of energy and resources to recycle paper, aluminum and steel cans. This is a simple fact. If it were not, you sure as hell could not get any cash for scrap metal or paper. Here in America, private businesses will not pay you more than something is worth. I could not say about plastic, but the raw material for making plastic is petroleum, which we should probably be more careful how we use.
The impetus of this little movie seems to be the report that this government guy put out saying we were running out of landfill space. Just because some government stooge says someting, does not make it true(eg, "I did not have sexual relations with that woman")
I like Penn&Teller, funny sons of bitches, loved their HBO show, Bullshit!, which very likely is the source of this little vignette. That said, they are largely full of shit on this one.