The DA-1 credit is designed to offset the US withholding tax, but Switzerland’s tax system considers your overall tax liability. If your taxable income is significantly reduced by deductions (like mortgage interest), your overall Swiss tax liability might be low enough that there’s little or no Swiss tax left to be “credited” against the US withholding. In short, they’re saying you haven’t paid enough Swiss tax to justify the full DA-1 refund. They are not saying the US tax is invalid, but rather that your overall tax situation in Switzerland does not warrant the full credit.
Mortgage interest is a deductible expense that reduces your Swiss taxable income. It is not directly related to the US dividends themselves, but it indirectly impacts your eligibility for the DA-1 credit by lowering your overall tax burden in Switzerland. This is a matter of Swiss tax rules, not US tax rules. The DA-1 is a credit against Swiss taxes owed. If your Swiss taxes are reduced by deductions, so is the amount of the credit you can claim.