Problem using CArrayDataProvider and CGridView when array does not have an 'id' field.

I have been trying to use CArrayDataProvider to format some array data to then display using the CGridView widget, however it does not seem to work unless there is a defined 'id' key in the array. This seems to me to be an unnecessary requirement, so I'm not sure if this is actually the case or I am missing something. As an example:

<?php $testArray1 = array(array(
			'user_id'=>'1',
			'name'=>'david',
			),
			array(
			'user_id'=>'2',
			'name'=>'andrew',
			),
	);

	$testArray2 = array(array(
			'id'=>'1',
			'name'=>'david',
			),
			array(
			'id'=>'2',
			'name'=>'andrew',
			),
	);

	$dataProvider1 = new CArrayDataProvider(
			$testArray1, array(
				'sort'=>array(
				'attributes'=>array('user_id'),
				'defaultOrder'=>array('user_id' => false),
			),
				'pagination'=>array(
				'pageSize'=>10,
			),
		));

	$dataProvider2 = new CArrayDataProvider(
			$testArray2, array(
				'sort'=>array(
				'attributes'=>array('id'),
				'defaultOrder'=>array('id' => false),
			),
				'pagination'=>array(
				'pageSize'=>10,
			),
		));

	$this->widget('zii.widgets.grid.CGridView',array('dataProvider' => $dataProvider1,));

	$this->widget('zii.widgets.grid.CGridView',array('dataProvider' => $dataProvider2,));

?>

The two arrays are exactly the same except that the id fields are labeled differently ('user_id' vs 'id'). The problem is that the array with the id field labeled 'id' will work (can be displayed by the widget CGridView), whereas that with the id field labeled 'user_id' gave me the following error:

PHP Error

Undefined index: id

yii_root/framework/web/CArrayDataProvider.php(99)

087         else
088             return $this->rawData;
089     }
090 
091     /**
092      * Fetches the data item keys from the persistent data storage.
093      * @return array list of data item keys.
094      */
095     protected function fetchKeys()
096     {
097         $keys=array();
098         foreach($this->getData() as $i=>$data)
[b]099             $keys[$i]=is_object($data) ? $data->{$this->keyField} : $data[$this->keyField];[/b]
100         return $keys;
101     }
102 
103     /**
104      * Calculates the total number of data items.
105      * This method simply returns the number of elements in {@link rawData}.
106      * @return integer the total number of data items.
107      */
108     protected function calculateTotalItemCount()
109     {
110         return count($this->rawData);
111     }

Any ideas? I can't think that it is a requirement to always have an 'id' field...