This did the trick:
$form = $this
->createForm(new UserType(), $user, array('method' => 'PUT'));
The method
bit was missing. Apparently, Symfony isn't cool enough to just get the parameters for you. When creating a form, you have to manually tell it what type of request it's dealing with. While this worked, I'm not sure that this is the best answer. I'm more than willing to hear others.