Sure, these things are related, but the article is correct to point out things like exports and capital investment.
If the US were producing more, even if all of the additional product were to be exported, GDP would be higher.
Any problem with GDP (or growth in GDP) is related to value-creating economic activity.
Yes, if the government were to spend (invest?) money in public works, GDP would rise, regardless of the output of the works. There would be secondary effects, too, as some of the money earned would be spent on locally-produced goods/services like lattes and haircuts.
Japan tried this: http://mobile.nytimes.com/2009/02/06/world/asia/06japan.html