They deduct ‘Kosten für die Verwaltung des beweglichen Privatvermögens’ (and interest on debt) from the gross dividends because you don’t pay taxes on that. This is done proportionally to your taxable net worth.
Let’s say you have invested CHF 100k in VT, have a VT gross dividend income of CHF 2000, have a taxable net worth of CHF 300k and have deducted CHF 600 for the management of your wealth. As your investment in VT is 1/3 of your taxable net worth, they will deduct CHF 200 (600/3) from the CHF 2000 VT dividends. This leaves CHF 1800 as taxable DA-1 earnings. Then they multiple this with your effective income tax rate, e.g. 20%. This results in a maximum DA-1 return of CHF 360. This is higher than 15% of CHF 2000, so in this example you get the whole CHF 300 back.
However, if you have relatively high deductions or a relatively low effective income tax rate, the maximum DA-1 return may be lower than the 15% of the gross dividend, in which case you get less back. The reason is that effectively the US taxed you more than Switzerland and Switzerland will never return more than what you pay in Swiss taxes (for the DA-1 assets).