I was exposed to this myth in my youth as various European nations described their misadventures in the US of A or encounters with Americans and as a result came to US with wrong expectations. Now that I live here, things a little more clear to me. It is a nation of more than 350 million people ( depending on how and who you count ). Even a small percentage of certifiable idiots will be very well represented in terms of absolute numbers.

I would not say Americans in general are dumb though. I would say that:

1) they are under-educated ( and then we can also get about the quality of education for those that were educated ) 2) they are very heavily propagandized