Again, Bitcoin isn't based on fiat, it's measured against fiat. The fact that people are willing to pay for it simply means that it's valuable as others have said. And even if Fiat goes to 0, the trust built up on the system of fiat is completely different from the trust built up by Bitcoin, and that's what makes it valuable, compared to those that have intrinsic value themselves. The only situation where Bitcoin would have no intrinsic value is when the people using it deemed it to be useless.