I teach third grade, but used to teach middle school. Even by first or second grade, students have internalized the message that it is better to appear to be skilled than to let people know your real reading level. With older kids, it gets harder and harder to convince them otherwise. But, it is possible!
I know that some teachers will let students continue to pick books that are not good fit as long as the student wants, so the students can really see what happens when a book does not meet their needs. I disagree with this approach after the first couple of week for a simple reason: Some of my students have never read a book in their actual "good fit" range so do not understand what it means to "know most of the words" or "understand" the book!
So for those students I think about their interests and curate a selection of books for them to choose from -- books that they are likely to be successful using, so that the idea of "good fit" finally makes sense. Once I have done this, and they experience success with accuracy, fluency, and comprehension, THEN I let them try with an unlimited selection again. Usually it only takes a couple tries at curation before the children consistently find books at a level that meets their needs.
Hope this helps.