I've found this to be decidedly not true, from many recruiter contacts. They have a role in mind they're trying to fill and if you point out that it's far more junior than what you're looking for, the conversation's over.
Think about how must companies hire. The hiring manager fights internally and finally gets a req for a very specific role. They have to fill that role. Having a generally smart person would be great but they have this immediate need and they can only hire one person. And once that req is filled, no more hiring until you get another req.
I'd love to see a company literally just looking to snap up smart people and then have them come in and kind of define their own role, one where they can add the most value. Nobody does this!