How to disable the default CAPTCHA packaged with Magento 1.9

Given that the custom extension does not extend Mage_Captcha and instead uses their own implementation, you can disable the core module entirely. Create a file app/etc/modules/Zzz_Deactivate.xml with the following content:

<?xml version="1.0"?>
<config>
  <modules>
    <Mage_Captcha>
      <active>false</active>
    </Mage_Captcha>
  </modules>
</config>