If a product key is activated on a machine then another product key cannot be used. That's just how it works.
The InnoSetup example shows that if a product key is already activated it doesn't prompt for a new product key. That's good behavior.
If you want to test from a "Clean slate" then you need to deactivate your existing product key first. Do that by calling the Deactivate() function. Also, shown in the InnoSetup example in the uninstallation script.