The judges who chose AES and SHA-3 as the "winners" of the global competitions are the NSA.
> You should avoid at all costs anything that has been standardized by NIST...
That would include AES and SHA-3.
Sure, however this process creates alternatives and if the crypto community thinks the winner is backdoored I am pretty sure we will know it and additionally we will have a valid alternative ready to be implemented. Additionally if the NSA/NIST modifies the specs for the crypto construction there is still the possibility to implement the original one. See SHA-3 for instance. It was about to be weakened, but the crypto community could still implement the original spec.
> That would include AES and SHA-3.
You cut the rest of the sentence and therefore changed completely the whole meaning. My original sentence included: "...without going through years of reviews by international cryptographers." Take a look at this video of D.J.B.: https://www.youtube.com/watch?v=G-TM9ubxKIg He makes a great example with the Dual_EC_DRBG, where many cryptographers told NIST that there could be a backdoor. NIST answer basically was: sorry too late, it has already been implemented !
So in other words, in case of Dual_EC_DRBG the standardization process was all in reverse. First NIST standardized it and then the crypto community started to review it and found problems.