I don't know about that particular case, but you are basically right: In Switzerland, if you want to apply for citizenship, you apply for it in the municipality first. Everybody having the citizenship of the municipality has the swiss citizenship as well. In theory, the canton and the state also have something to say, but that's irrelevant for most applications.
This has historic reasons, but going into the details is beyond the scope of this question.
Fact is, that every municipality has its own rules, about when and how applications are handled. This has been unified a bit in recent years, but some things still differ. That is for instance, how many years you need to have lived there or who decides your application. There were municipalities (actually most) where the final decision was made using a public vote. This practice was declared illegal by the federal court some years ago, because becoming a citizen is a formal governmental act, and as such a reason needs to be given for turning an application down. This is inherently impossible with a vote.
Since that law decision, most municipalities have shifted the responsibility to a committee for citizenship applications. The public can still bring in arguments, but they need to be justified (ie. if somebody knows about the applicant being a wanted criminal somewhere).
Consequently, you can now call for a court to check whether the given reasoning is correct and just, if you are turned down.