The NSA is not going to tip its hand about any backdoors it had built into the hardware for something as small as this.

It depends on if parallel reconstruction can be used to provide deniability.

Even a parallel construction has limited uses, since you can't use the same excuse every time. The NSA probably doesn't trust the FBI to come up with something plausible.

That depends on how apathetic people are. Most of the time they will accept a completely garbage story and you can create infinitely many of those.