That line is more false than true. For the most part they are not recycling their trash, they are incinerating it.
Additionally Sweden is tiny. Trash there is brought to local recycling centers with 6 to 8 or more different bins, and people are expected to sort their trash.
How would you do that in the US? Trucks with 8 compartments? Where would you even keep that many different trash cans? The US is very large, you can't expect people to transport their recycling.