The backdoor in the EC DRBG algorithm was detected but never leaked because to actually open that back door required a key only the NSA had, but that key itself never leaked. Only the NSA could decrypt streams that used this PRNG. To everyone else they remained undecryptable.
So it's not a counter-example and your amusement is misplaced.
Yes. It's simple, if you send information in a recoverable way to another entity, they can recover it. If that entity involves humans, they can and will with 100% certainty be corrupted or threatened to obtain the information improperly.
> Remember the kerfuffle over the NSA's backdoored ECDRBG algorithm?
Amusing that your example is a counterexample to your thesis. Exactly. Backdoors never serve only their would-be masters. That's the impossible part.
If this is not blindingly obvious by now, I fail at being able to explain it better.