Backbone is event-driven library so it is best practice to use events to make parts of application less coupled. So you can trigger event on your view when some button is clicked and listen to it in some kind of controller/mediator - object that know about peaces of your application and can change input when button is clicked.
var ButtonSetController = _.extend({
start: function(){
var buttonSetCollection = new ButtonList([{val: "A"}, {val: "B"}, {val: "C"}]),
buttonSetView = new ButtonListView({collection: buttonSetCollection});
this.listenTo(buttonSetView, "button:clicked", this.onButtonClicked);
$("form").append(buttonSetView.render().el);
},
onButtonClicked: function(button){
$("input").val(button.get("val"));
},
stop: function(){
this.stopListening();
}
}, Backbone.Events);
ButtonSetController.start();
Here is code: http://jsfiddle.net/8aY3M/