This makes sense. In summary, it means I am only eligible for the Anrechnung ausländischer Quellensteuer part of the DA-1 (15%) and may have incorrectly also submitted the Antrag auf Rückerstattung des zusätzlichen Steuerrückbehaltes USA using the R-US 164 form. I believe this is somehow integrated into the DA-1 form in the canton of Thurgau. Since the R-US 164 form only applies to Swiss brokers (who actually withhold the additional 15%), and not to IBKR (where I submitted the W-8BEN to reclaim this withholding tax), my claim was denied. Good to know for my next Steuererklärung 
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I suppose everybody (including myself) made this error. In Zurich it was just ignored when you made the cross at “zusätzlicher Steuerrückbehalt USA”.
However, you should get back your Swiss tax on dividends if your tax rate is lower than 15% or 15% if it is higher. In Zurich the two departments do not speak with each other, you have to pay and then get it back at your bank account. Since you can declare online however at least you don’t need to send in everything twice any longer…
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