drupal_render ignores checkboxes form array default values

I am able to get some html form checkbox inputs to print using drupal_render($form['pizza']), but the default values that I want to be checked on page load are ignored. Running $form['pizza'] through form_process_checkboxes() adds '#options' key array elements to the $form['pizza'] array, which is needed to get drupal_render($form['pizza']) to create the html checkbox inputs. If I don't add the '#value' key to the $form['pizza'] array I get the following error:

Notice: Undefined index: #value in form_process_checkboxes() (line 3314 of /var/www/mysite.com/htdocs/includes/form.inc).

The form_process_checkboxes() code uses the '#value' array to add '#default_value' values to the option key array elements that are added to the $form['pizza'] array in the form_process_checkboxes function. Those '#default_value' values do not result in "checked" identifiers being added to the html inputs that are created by drupal_render($form['pizza']). I am not using the standard hook_form functionality because I am creating the checkbox inputs in a views template file so that I can use the inputs along with jquery to control different images that appear on the page.

Is there a way to get the default checkboxes to be checked on page load using drupal_render() without creating the output using drupal_get_form() and the hook_form function? Maybe with multiple '#type' => 'checkbox' $form arrays instead of 1 '#type' => 'checkboxes' $form array? Or by creating the wrapper that is added to the $form['pizza'] array by drupal_get_form() without the hook_form function? I understand that there are other ways to print checked html checkbox inputs in a template file, but at this point I am pretty curious about why the '#default_value' values are ignored by drupal_render after being added in form_process_checkboxes().

$form['pizza'] = array(
	'#type' => 'checkboxes',
	'#title' => 'Toppings Choices',
	'#title_display' => 'before',
	'#attributes' => array(
		'name' => 'pizza[]',
	),
	'#value' => array(2 => 'Sausage', 3 => 'Mushrooms'),
	'#options' => array(1 => 'Pepperoni', 2 => 'Sausage', 3 => 'Mushrooms'),
	'#default_value' => array(2,3),
);

$form['pizza'] = form_process_checkboxes($form['pizza']);
$html = drupal_render($form['pizza']);
print $html;