My Mage_Shell script doesn't work: Mage::getModel() can't find class

Question

So, I just ran into this and scratched my head quite a few times and since the Magento bug tracker is dead, let's do it here.

Symptom:

Class 'MyNameSpace_MyModule_Helper_Data' not found in /var/www/example.com/app/Mage.php on line 547

This happens when a script is run, based on shell/abstract.php. The site works fine, so I know that the helper/model/block is working. What's going on?