I wouldn't call bitcoin being paired with fiat as dependency but rather a manifestation of bitcoin's value in fiat. Like gold and oil having their value in fiat, I see that as the same with bitcoin. You can't say that bitcoin is fiat-dependent given that it continues to produce its own coins without fiat's interference. However, the whole economy, together with the traders and the miners are the ones who are dependent with fiat, not bitcoin directly. If you remove fiat into the equation of the economy, people might lose interest, though they can still use bitcoin if they so do wish and if there are still people believing in its value. Fiat is a vital part of the economy, but not the inner workings of bitcoin, I'd say.