It's fair to say that we ought to be able to pass the tests we ask other people to take. The U.S. citizenship test has traditionally had enough oddball questions in its question pool that I suspect many citizens wouldn't actually pass. Now it's been revised, and the Times surveys a range of ideological responses to the changes -- some immigrants groups are outraged, etc. However, if you look at the actual exams (the new exam question pool is here; a comparison of the new and old exams is here), it seems clear that the new exam is a huge improvement from the point of view of mechanics: the clarity and phrasing of the questions is now much, much better.
For example, one old question was "Where does freedom of speech come from?" What is that asking, exactly? Another bad one: "Why are there 100 senators in the U.S. Senate?" It's obvious what is meant (50 states X 2 senators per state), but the phrasing is bad. It's now so much why as how you get 100 senators.
Another poorly phrased question from the old exam is "What are some of the basic beliefs of the Declaration of Independence?" Again, it's a bit strange to refer to the "beliefs" of a written document. Better phrasing might be, "What are some of the principles expressed in the Declaration of Independence?"
Among the new questions, there are very few that have these kinds of problems. Admittedly, some of them are a bit more difficult from a straight historical perspective ("What territory did the United States purchase from France in 1803?"), but it's not hard to go learn (and yes, memorize) the answers.