I think your understanding is mistaken, or at least regional. While it can mean "parents" when used in the plural with a possessive ("my folks", "your folks", sometimes even "the folks"), in modern American English it's as commonly just a synonym for "people".

Using "folks" (especially in the plural) to mean people can be rather "folksy", though, and I wouldn't be too surprised if some textbook or dictionary mentioned just the "parent" definition. Did you learn it this way as a second language, or as a native speaker somewhere non-American?