we are measuring it's value in dollars.
and what would you suggest we use to measure its value? it is the 21st century, we measure value of literary everything in fiat, those in US measure it in USD, those in Europe measure it in EUR, those in China measure it in CNY and ....
that doesn't mean it relies on fiat. would you like us to go back a thousand years and measure value of things like bitcoin in goods? like saying 50000 satoshi is equal to 1 chicken?
Well, that is a smart answer! Great answer!
At present, all valuables are valued and measured with fiat money, in other words, all depend on fiat currency. Obviously, that is the way we determine everything right now.
I think, what is meant by the independent nature of Bitcoin is the fact that bitcoin does not depend on the government, Bitcoin runs without the central authority or third parties.