You have to declare and set the idAttribute
of your model:
class MyApp.Models.PulicFile extends Backbone.Model
urlRoot: '/public_files'
idAttribute: 'yourId' // or the default value 'id'
and then in your model instance, set the id and fetch the model:
yourModel.set('yourId', theIdValue);
yourModel.fetch();
Now you will get the url that you want /public_files/ID