As others have replied, that is perhaps an antiquated perception.
I think the theory also comes from the fact that the Big 3 seem to have many more recalls than foreign companies. However in recent years, Toyota has actually recalled more cars than any other company [1]. Recalls are most often initiated by the company and not the government and therefore stats can change depending on the willingness of the company to start a recall (as seen by GMs recent problems). Anecdotally, the Asian car manufacturers rarely ever publicly announced recalls and would simply perform the recall when you took your car in for service. Therefore customers never knew there were issues and they were branded as "reliable" cars when perhaps they shouldn't have been.
I've always found JD Power to be a bit biased towards American made cars. Maybe because he worked for Ford and GM, I don't know, but even at their worst, they always seemed to be featured by them.
I have been utterly unimpressed with the Silverados and Avalanches. For that kind of money, I expect a lot more than fragile/cheap interiors (Silverado) and the crummy bed on the Avalanche.
Ford seems to have really cleaned up their act the last 3-5 years. I'm still a bit wary of Dodge/Chevy/GM, but have been super impressed with Ford. Granted, Ford did stink it up something ferocious in the early-mid 2000's.
Completely anecdotal, but we bought a 2012 focus last year and have been incredibly happy with it. Far more than with the Honda Civic it replaced. We run the wheels off our cars, and it's been a real trooper. Good gas mileage, easy to work on, cheap to repair/maintain.
And if it's anecdotal quality you're speaking of, try again there too.
I drive a German car, I'm not an American car apologist, but there's no question that the "big 3" have stepped-up their game.
Not to mention, all the Japanese, Korean and even some European cars you mention are actually built in the US.