Yes, allowing you to do that was a Steuereintreiberfehler.  That provision of the treaty is not there for your benefit. It's Germany reserving the right to tax rental income, even when there might be an exception for other income earned by nonresidents.  The United States did not give up any right to tax the same income, but the Internal Revenue Code still allows the foreign tax credit, to avoid Doppelbesteuerung.  

You have been paying German taxes, nicht wahr?