No. It is up to whatever DNS server your computer asks. You could easily set up your own. The issue is that when you buy a domain name, it gets entered into ICANN's root servers. It used to be (and may be again, I haven't checked in a while) that you could download all of that information in one fell swoop, though. So you could set up your own root servers that have all of that agreed-upon information plus whatever else you wanted to put in there, but no one would know about it but you and anyone else you told to use your new root servers. So, the issue is do you want to use the root servers everyone else uses or do you want to use ones that no one else uses? Since the Internet is a cooperative, the former seems a better idea, but there is no technical limitation preventing you from doing otherwise.

There does seem to be a US bias in ICANN, but that seems to be more of an endemic organizational bias than as a result of influence from the US government.