It used to be illegal for Americans to deposit money with some of these things, because they were basically tax scams, although I don’t believe it’s illegal anymore. And while I think taxes are way too high, if I have to pay them from my modest income in the US, I think somebody who made his huge income here in the US should have to pay them, too...but the Cayman Islands were where you went not to pay them. This is the reason Romney does not want to release his returns.
It’s all perfectly legal, but offshoring your huge fortune sure doesn’t make you look good.
With minor exceptions, Americans pay taxes on earnings everywhere in the world under American law. I suspect this is more a function of bypassing security regulations. You're correct, it doesn't look good.