The value of the transaction network is highly dependent on the exchange value. I'm not sure exactly what you mean when you call it distinct, but miners will certainly respond to changes in the exchange value, which may end up removing much of the vaunted security of the ledger (which removes interest, which makes mining less lucrative, which ...).

(I don't necessarily think there is strong case for those scenarios, but it's pretty hard to decide at what exchange rate the thing becomes unstable).