You Don't Know Where Your Interest Lies

The title, by the way, comes from a Simon and Garfunkel B-side but that's beside the point or on the other side of it as the case may be.
There's a lot of discussion now about creating educational settings that are focused on student's interest.  One popular video making the rounds of teacher meetings highlighting the need for teaching 21st century skills stresses that students have to be engaged by curriculum that fits their interests.  Thinking back to my days in elementary school I think I would have liked to have more going on in class that fit my interests, trouble is I can't honestly say what my interests were then.  Was I primarily interested in what would happen in the next issue of Batman? yeah, that's likely.  Was I interested in what the new Beatles record would sound like? of course.  So what would a curriculum founded on Batman and The Beatles have looked like, well we know it would have sounded cool, but what would it teach?
As a teacher today I listen to kids talking about what they're interested in all day.  They write about the things they care about, they share about the latest game they're into or the movie they saw over the weekend.  We look for connections between the various dots of young people's diverse interests and pull those into the rest of our curriculum.  For example Spongebob, I've discovered, provides an excellent opportunity to practice classifying and organizing creatures when talking about exoskeletons.
But here's what I'm wondering today.  Is organizing curriculum around student's interests a backwards way of doing things?  Should schools be primarily oriented around teaching a wide variety of skills and a broad knowledge base so that kids can develop "interesting" interests?  Any school that I've ever worked in has provided plenty of opportunity for students to express their interests and make connections between prior knowledge and whatever the subject that is being studied.  What do you think?  Should we orient curriculum more around what kids are interested in when they walk through the door, or should we create curriculum that aims to give them plenty of interests when they walk out the door?
Most likely it's a mix, but what is the recipe?