Get customer account data in shipment PDF

Question

In the Invoice PDF I can get (logged in) customer account data with the following code:

$customer_email = $order->getCustomerEmail();
$customer = Mage::getModel("customer/customer"); 
$customer->setWebsiteId(Mage::app()->getWebsite()->getId()); 
$customer->loadByEmail($customer_email);

If I try to use this code in the shipment PDF (Mage/Sales/Model/Order/Pdf/Shipment.pdf), the customer data remains empty.

Given the customer email in $order, how can I get the account data in the shipment PDF?