How is a field's value (rather than its key) obtained?
As you can see, you pass to field_get_items() the $node parameter. This should tell you that this function will return you a value stored in this Entity. The values of your field are stored in the field itself. You can get your options array as following.

$fieldData = field_info_field('field_group');
$options = $fieldData['settings']['allowed_values'];