The best way to argue against this idea is to point out that government bears a great deal of responsibility for whether people vote.
The choice to vote is (according to political scientists) made on the basis of a cost-benefit analysis. Voting costs time because voters must become informed on the issues and candidates and must actually take the time to go to the polling place. Voting only carries a benefit if voters feel that government actually works for them. Therefore, the more that people feel the government does not respond to them, the less likely they are to vote. If a voter feels like her voice is never heard because the government responds only to the big companies, she will not bother to vote. This is something that is in the government's control, not that of the voters.
Thus, the decision not to vote does not come simply from laziness. Instead, it comes about in part because of the government's own actions. This means that people have the right to complain regardless of whether they vote.
Three other arguments come to mind for me to support peoples' right to not vote and yet complain. First, in a two-party system, when people do vote, there is a 50% possibility that the candidate they vote for will not win, thus placing them in the position of not having their interests represented. There is a certain amount of time and energy one must invest in order to vote, and it might seem perfectly reasonable for a person to not vote because the odds are so poor, with a concomitant belief that complaining is reasonable because of the odds he or she would have been complaining anyway. The second point is that our right to complain is not based on our exercise of our voting rights in the first place, but on the First Amendment of the Constitution, or at least our right to not have the government interfere with our right to complain. There is no real logical or legal connection between our voting and our right to complain. Finally, the fact that people complain in spite of not having exercised the right to vote does not mean their complaints have no value. There are thoughtful people with good ideas that do not vote. Their right to speak is not dependent upon the exercise of their right to vote.