Adult readers never seriously maintain that fictitious characters exist

A) "Never" is a strong word. I imagine there are all kinds of mental disorders that can lead certain adults to confuse fiction with reality

B) "Existence" here is a cached term used for simplifying a concept to the point of being inaccurate. When a person says that, for instance, Frodo Baggins doesn't exist, he or she would be entirely incorrect to say that there is nothing in existence that matches the concept of Frodo Baggins. What the person is actually saying, is that a description of the character of Frodo calls to mind an image of something resembling an organism and that this image fits into a mental category that no actual organism can fit into. Whether or not Frodo "exists" is a pretty poor question unless fleshed out.