I'll take you up on that.
Here's Schneier on ECC:
https://www.schneier.com/crypto-gram-9911.html#EllipticCurve...
He wrote this in 1999; ECC was at the time sort of a novelty, it's headline being "a way to do cryptography with smaller key sizes", as if ECC was mostly a way to fit crypto into smaller memory software.
Schneier and Ferguson wrote _Practical Cryptography_ in 2003. It has virtually no mention whatsoever of ECC cryptography, despite ECC's already significantly increased importance by then.
In 2013, I think it's fair to say that the balance of expert opinion on ECC vs. RSA is sharply against Schneier's take on ECC. RSA is on the way out, and ECC is what's going to replace it. Equally significantly, crypto constructions that use signing and key agreement but not public-key encryption/decryption operations are modern designs; designs where a long-lived RSA key is used to wrap and unwrap secrets are dated. ECC is useful for the modern constructions and less so for the dated ones.
I don't think Schneier's writing has tracked these shifts well. I think his books are very light on, for instance, forward secrecy or deterministic signing. His research results never focused on public key encryption and never touched ECC (it's worth noting that much of his best known research was also done with John Kelsey, who is at NIST --- coincidentally, one of Schneier's best-known designs, with Kelsey, was the Yarrow CSPRNG).
Also: Schneier has a close working relationship with Niels Ferguson, who was one of the researchers that spotted the weirdness in Dual_EC. So it's possible that Schneier's concerns over the "constants" in ECC all stem from that. (It's hard to say; he could also be referring to the random seed in the P-224 and P-256 curves).
I don't think readers have any particular reason to believe that Bruce Schneier is an authority on ECC.
Cryptography is not one topic. It's actually a little silly to suggest anyone like Schneier could be authoritative on all crypto concepts. Look at the research output of famous cryptographic researchers (Schneier has some research, but is not really a top-tier researcher) --- it tends to specialize!