Brokers are often limited in which countries they'll accept clients from, but that's to avoid all the overhead of filling the appropriate tax forms to each government (and maintaining the knowledge of what the rules in each country are).
That's exactly my point - Etrade already does all the tax forms for me, I don't understand why they won't allow me to have a full account. Probably some "blanket policy".
As for Amazon, I would expect them to eventually expand globally if they were to offer such services (which is not what I expect from most US brokers).