"NSA has been breaking codes (not merely wiretapping) since NSA has been around, just like it has long been an open secret (if unacknowledged publically) that NSA hacks into specific systems if they can."
BULLRUN is not a cryptanalysis program, and it is a stretch to call it a "hacking" program -- and certainly not one that targets specific systems. BULLRUN is the NSA program to deliberately introduce exploitable bugs in cryptographic protocols, software, and so forth.
"the history of NSA has shown them before to be willing to give people cryptosystems that are strong against everyone but the NSA."
First of all, the NSA does not frequently give cryptosystems to anyone outside of the US government. That being said, there are two prominent counterexamples to your statement: DES and DSA.
"I thought the ever-present distrust of NSA was exactly why they looked for backdoors in things like Dual_EC_DRBG, and used "nothing up my sleeve" constants in algorithms designed in academia."
It is worth noting that even when the Dual_EC_DRBG backdoor was discovered, there were people who were skeptical about it being deliberate. Even Bruce Schneier expressed some skepticism about it being an NSA backdoor:
https://www.schneier.com/blog/archives/2007/11/the_strange_s...
I don't understand why the NSA was so insistent about including Dual_EC_DRBG in the standard. It makes no sense as a trap door: It's public, and rather obvious.
As for nothing up my sleeve constants, that goes beyond just showing that there is no back door. Suppose you were analyzing a cryptosystem, and it required some particular constant. What about that choice of constant makes the system secure? If a different constant were used, would system still be secure? Even if you never gave any thought to backdoors, nothing-up-my-sleeve numbers would matter -- cryptographers like to know the reasoning behind design decisions, and it is much easier to explain why you picked 1234567890 as a constant than 43895762356157265.