I'd definitely say American drivers, as a whole, are less prepared for and take too lightly the responsibility of driving a car. It is far too easy to get a license in this country: My test consisted of me, at sixteen years old, going around a suburban block with very little traffic at about 35 miles an hour, followed by a brief parallel parking test (a test I consider far less relevant than, say, being able to merge on a busy freeway at high speed). To qualify for this test, I only had to purchase an online driving course and fill out forms claiming that my parents had been me with me while I drove - none of which required time with a trained instructor.
Contrast this with China - one of the countries that you listed as an example of having bad drivers - where to obtain a license you need to pay the equivalent of a few thousand USD for a rigorous driving course in an isolated area (you can't even drive on the road before you have your license; learner's licenses do not permit you to drive on public roads). After this, you are still under some limitations until a year after you've obtained the license.
In addition to this, the more aggressive driving culture of China involves many more vehicles jostling for smaller spaces than would be the case in America. The skill and spatial awareness of the vehicle necessary to cope with this sort of environment is far greater than that needed to deal with even the most demanding driving environments of America.
We are definitely more laid-back and polite in driving than China (and I would prefer that any day) but more skillful? I highly doubt that.