I gather your question is more about privacy than about DNS, so here goes.
Don't consider ANY surfing as anonymous. Your US-based ISP is required for some time now to log all activity (Yes, I said, *required* as in law).
This info is supposed to only be available via a court order.
The only way to avoid such pitfalls is to strong encrypt your datastream to a system that acts as an anonymous proxy. This, too, is subject to the same laws, even though some claim they will not release your info. (They have to know your IP info, else you couldn't connect