...unless that is, in 2005 the NSA installed a PRNG backdoor in the AES-256 SHA-3 "NIST-approved" protocol for encryption, as Bruce Schneier et al. have shown long ago is highly probable.
I do not believe that the NIST changes were suggested by the NSA. Nor do I believe that the changes make the algorithm easier to break by the NSA. I believe NIST made the changes in good faith, and the result is a better security/performance trade-off. My problem with the changes isn't cryptographic, it's perceptual. There is so little trust in the NSA right now, and that mistrust is reflecting on NIST. I worry that the changed algorithm won't be accepted by an understandably skeptical security community, and that no one will use SHA-3 as a result.
So Schneier explicitly says he DOESN'T think there's a backdoor in SHA-3. WTF you talking about.
What's more, a SHA exploit does not allow anyone to steal coins, it only affects mining. ECDSA is what protects transaction signing and thus the coins. AND even if that were broken you still couldn't steal coins from addresses which had never been spent from, because you don't know the public key.