Zusätzlicher Steuerrückbehalt / Retenue supplémentaire USA (R-US)

I just received my Veranlagungsentscheid for 2022 from the TG tax authorities, and it looks like my DA-1 refund claim was denied. They’re now asking me to repay the Verrechnungssteuer in full.

The only explanation provided was:

Formular DA-1: Der zusätzliche Steuerabzug USA (USR), kann nur auf Erträge bei einer Schweizer Depotstelle zurückgefordert werden (Sonderabkommen Schweiz - USA).

Has anyone experienced something similar? Is this interpretation actually correct, that the US withholding tax (USR) can only be reclaimed via DA-1 if the assets are held with a Swiss broker?