ng-checked creates a one-way data binding, so the model does not get updated when you toggle the radio buttons.
If you're using radio buttons, you still need to use ng-model:
<input type="radio" ng-model="selection" value="0"/>
<input type="radio" ng-model="selection" value="1"/>
<input type="radio" ng-model="selection" value="2"/>
When the user selects a radio button, the model is set to the button's value.
(I've added some application logic to the controller to query which radio button is selected. This is used for the ng-disabled check.)