The truth is somewhere in between. We overextended ourselves during the Cold War and afterwards, and it wasn't for the sake of freedom. It was for money. Opening trade with China at the height of the Vietnam War was a good example of this.
On the other hand, China isn't as harmless are you're implying. They are quite good at the "soft power" approach, but that involves corrupting governments rather than overthrowing them (usually). Their model is a lot like what Europe did after it officially dropped its African colonies. It is true that the Chinese really don't care about exporting their culture, but they are more than happy to extract your resources until they are gone.