I can only cite McGrath: What on earth is the problem?
There is nothing anti-American in this quiz with the exception of a very unfortunate wording of the BBC's link.

Insert any other nation as the target nation and you'll see that easily. Many questions are merely knowledge questions. And for the other questions, without any control data you even cannot be sure that the responses reveal any significant amount of anti-Americanism. Ask for instance whether Russia is seen with more approval than disapproval in six Moslem countries, and you may also find that only one country (though perhaps not Uzbekistan) has more responses in favour. Perhaps no country in this world of any significant size finds more people in many other countries being in favour of it.

The data are completely irrelevant for the title question of this thread. But still, it is an interesting quiz.

Wolfgang