Magento – How to we add/update a image path with own code without using addImageToMediaGallery()

Try passing an array as the media type. Theer is no need to iterate over each mediaType and setting them individually.

your code would thus be, which will be faster as well.

ini_set('memory_limit', '-1');

require 'app/Mage.php';
Mage::app();

echo "Loading catalog...\n";
$products = Mage::getModel('catalog/product')->setStoreId(13)->getCollection()->addAttributeToSelect('*');
echo count($products) . " products selected for image import.\n";
// Remove unset images, add image to gallery if exists
$importDir = Mage::getBaseDir('media') . DS . 'import/';  

foreach ($products as $product) {
        $sku = Mage::getModel('catalog/product')->load($product->getId())->getSku();
        if (strstr($sku, " ")) {
            echo "Sku $sku contains whitespace, skipping.\n";
            continue;
        }
        $imgFile = $importDir . $sku . ".jpg";
        // Add three image sizes to media gallery
        $mediaArray = array(
            'thumbnail',
            'small_image',
            'image'
        );
        if (file_exists($imgFile)) {
            try {
                $product->addImageToMediaGallery($imgFile, $mediaArray, false, false);
                $product->save();
                echo "Sku: $sku updated.\n";
            } catch (Exception $e) {
                echo $e->getMessage();
            }
        } else {
            echo "Could not match image to $sku. Path was: {$filePath}\n";
            break;
        }
    }

Anyways, I suspect your issue is related to the fact that your product->save was within the media loop of your original code.

For reference, the end-point of the mediaAttribute is this function, located in class Mage_Catalog_Model_Product_Attribute_Backend_Media

/**
     * Set media attribute value
     *
     * @param Mage_Catalog_Model_Product $product
     * @param string|array $mediaAttribute
     * @param string $value
     * @return Mage_Catalog_Model_Product_Attribute_Backend_Media
     */
    public function setMediaAttribute(Mage_Catalog_Model_Product $product, $mediaAttribute, $value)
    {
        $mediaAttributeCodes = array_keys($product->getMediaAttributes());

        if (is_array($mediaAttribute)) {
            foreach ($mediaAttribute as $atttribute) {
                if (in_array($atttribute, $mediaAttributeCodes)) {
                    $product->setData($atttribute, $value);
                }
            }
        } elseif (in_array($mediaAttribute, $mediaAttributeCodes)) {
            $product->setData($mediaAttribute, $value);
        }

        return $this;
    }

You can get the image, thumbnail and any other image attribute value from the product directly.

$image = $product->getImage();
$thumb = $product->getThumbnail();
....

Try to view product and image as 2 separate entities in a 0 to n relation.
A product can have o to n associated images.

But the image, thumbnail and small image are product attributes. They have no meaning in relation to the media gallery.

So you cannot get the value of image attributes based on media gallery values only.
If you need to find which media gallery acts as small image you can loop through the media gallery images and compare the $image['file'] with $product->getSmallImage()