Sure, but we're not talking about fixing the rate of CPI growth (stock prices aren't a constituent part of that and don't have a fixed relationship with it).

We're talking about the effect of wealth holders wanting more of their investments in stocks or more of them in cash on the USD. An increase in demand for the liquidity of currency holdings, or an increase in demand for stocks due to perceived improved returns could affect the dollar through knockon effects on availability of credit, but the interest rate for that credit is the price of the bit the Fed fixes.