The value is that (ideally) they've asked around and figured out how half a dozen peer firms do what you're struggling with. So while they may not have solved your management problem personally, they can give you an idea of what's worked for your peers without all the icky industrial espionage and antitrust violations you'd need to find it out yourself.
Where did they learn what’s changed in best practices for fast food logistics since the last time they consulted for Burger King? Well, funny enough, they were recently engaged by McDonalds…
This. You can have an open acknowledgement that the consultant knows jack as long as they can give you the sourcing of their underlying insights and best practices and it passes the sniff test.