Is there a hook to process a backbone restful PUT request inside wordpress?

The dynamic wp_ajax_ hooks serve mostly organizational convenience on PHP side.

You could choose not to use it, then you would probably have to:

  • hook into admin_init
  • check that DOING_AJAX is true
  • check that request ($_REQUEST['action'] and rest of it) is your special kind of request

Then either process your request and die() or let anything else through to normal handling.