Does "La Suisse" refer to the country or to the Swiss people? I suppose here it refers to the country (using the 3rd person singular "a"), but to say the Swiss people, we'd need to use the 3rd person plural "ont." Please correct me if I'm misconstruing this.
You would also need to pluralize the subject: "Les Suisses" to refer to the people. Of course, "la Suisse" can also refer to a Swiss woman, but it's hard to imagine a single person owning villages in Switzerland.