The concept of ownership is an ambiguous one, anyway. (I actually meant to add a paragraph to this effect in the original post. Oops.) If by "owning" we mean that it is ours, and ours only, and we will charge anyone else to look at it, then I don't think anyone can own folklore. (Although, by having copyright laws, society is saying that the creator of a work of art can have an amount of ownership of it.) However, the word has a wider use. For example, at work we talk about aiming at an ideal "young people feeling ownership of the library." It doesn't mean that they physically or financially own it, just that the have a say in how it develops - and, more importantly, that they feel it is theirs. Using the latter definition, I think we can say truthfully that folklore is "owned" by the people.