Analyze the role.
The conclusion of this rather tricky argument is stated first: in terms of politics, people's actions often do not match their words. The proof is an involved example which itself concludes -- in the last sentence -- that voters reelect politicians whose behavior the voters don't like. The important thing to realize is that everything beyond the first sentence is an elaborate example of people not doing what they say. It leads up to an intermediate conclusion, but don't be fooled by the "thus" and assume that the last sentence has to be the final conclusion.
The reason that the rest of the argument, including that last sentence, is proof for the initial and ultimate conclusion is that it shows people saying one thing -- that they dislike government intervention into their lives -- but then doing another -- not reelecting the politicians who stay out of their lives. Since political activity is equated with interventions in voters' lives, we can say that these people are not reelecting politicians who shy away from intervening, a choice which seems strange since these voters supposedly want politicians to stay out of their lives).
The question asks what role the fact that people don't vote for inactive politicians plays in the argument. As (B) notes, that piece of information is leading to the intermediate conclusion presented in the last sentence of the argument. This answer is tempting to incorrectly eliminate because it does not refer to that conclusion as an intermediate conclusion, however an intermediate conclusion is a conclusion nonetheless.
(A) is tempting, since the conclusion does relate closely to that fact, however the final conclusion does not explain that fact, and actually, the conclusion does not explain the intermediate conclusion. The intermediate conclusion is an example--a sort of premise--given to support the final conclusion. While a conclusion can explain a premise (dogs are violent, thus it must be that canines descended from wolves), but in this case, the fact that political behavior doesn't match rhetoric doesn't explain the discrepancy, it uses that as an example to generalize.
(C) is incorrect because people not voting for inactive politicians is not an example of politician's actions consisting of interference. The two facts are used in conjunction to build the intermediate premise.
(D) is incorrect because people complaining about government intervention does not lead to people not voting for inactive politicians. If anything, those complaints would lead us to expect that voters would vote for those politicians!
(E) is tempting but too extreme. Nowhere does the argument state that people's behavior NEVER matches their beliefs.