Again, you're not really being asked to trust NIST here, so much as you are the CRYSTALS team. If you think the CRYSTALS team has been subverted by NSA, you're pretty far outside of the mainstream of cryptography thinkers; notably, this isn't a claim Bernstein has made, or is likely ever to make, unless someone dares him to†.
† https://news.ycombinator.com/item?id=10376951