I think a closer analogy would be a Republican telling you that "Republican" is defined as someone who supports small government—and therefore libertarians are Republican (and most Republicans are, in fact, not Republican.)

There's an older version of this debate, regarding whether people who don't know or care about a given religion—but happen to follow all its tenets by coincidence—will get into the "good afterlife" of that religion. There are a lot of Christians who argue that to be "Christian" isn't a matter of faith, but rather a matter of acting the way Jesus would have one act. (And thus, in this model, there are atheist Christians.)