I have my own completely unsupported theory on why this is (Granted as an immigrant myself I might be biased). I think it is just a matter of selection bias. It is always easier to stay where you are and keep doing what you have always been doing. By taking the initiative to migrate to another country, no matter what the reason, you already have shown quite a lot of initiative to take a plunge into the unknown. This is very similar to the kind of trait that would cause a person to try to take a leap and attempt starting their own business.
I would guess that if you look at almost any country in the world you will find a higher number of entrepreneurs from immigrants precisely for this reason. I very much doubt that Americans would be less adventurous in this respect than any other culture. In fact I would be surprised if the difference isn't more pronounced in other countries precisely because the culture in this country if anything puts a higher emphasis on the virtues of being your own boss and owning your own business than in other places.