Earlier quoted context omitted.
The question is not whether BCrypt is backed by Blowfish, the question is whether BCrypt uses Blowfish in a way which is cryptographically sound. If it does not, then an attacker may not need to use brute force. Assuming the author has read more of Mr. Schneier's book than the quoted preamble, he should know this -- Schneier discusses this at length in both editions of Applied Cryptography . Again, an example of this…
You're speculating about the existence of a flaw which is there no evidence to believe could exist. Just because some crypto constructions are not as sound as naive theory suggests does not mean all constructions are flawed, or even capable of being flawed. bcrypt is not an encryption algorithm. It doesn't "protect" your users' data, so there's no reason to trust or not trust it with their data.
If you don't believe me, consider this hash function
H(A) = (A>>1)&0xFFFFFFFF
There. Hash function. It sends any input to a 32 bit value. Would you use it for your password though? No. I certainly would not.
Granted, that is an incredibly weak example, but it's one that's easy to see why it's weak, and thus why a hash function does protect a user's data.