Are 民谣 Songs? Or are they saying?
民谣 could be the following things:


民间歌谣 or rhymes of the folks. Chinese 歌谣s don't have to carry tunes, but they usually do rhyme, or at least carry some tonal quality which makes them sound good. They usually carry some sort of folk wisdom. Sometimes they are also called 民谚 or 谚语.
Regional folk songs. They are created and sung by common folks, and they do carry tunes. More often they are called 民歌.
Short for 独立民谣 or Indie Folk, the music genre becoming popular since 1990s. It's probably the most common usage nowadays.


Somewhat related: 儿歌 and 童谣 are 歌谣 for kids, they don't have to carry tunes, either.

As for your example, it's clearly just a saying, not part of a song.