Wrong problem.
The problem isn't that they think they are more qualified, it's that American companies think they are more qualified!
OK, you nailed it. BTW, my wife is on the phone with a bunch gooks in China that are taking over a business unit from an American company. She has been working normal business hours plus dealing with China and the Philippines every night. There is no way, these people have what it takes to innovate or even deliver the same quality of service to customers in the US.