Allegedly Apple wanted this request from the FBI to stay under seal, and it was the FBI who pushed to make it public. If that's the case, then it may have indeed been the FBI not Apple who turned this into a PR situation.
Somebody inside the FBI was greedy for a raise and took the risk to try to take a bite out of the Apple. I doubt they got demoted or took a salary hit. The career upside for the individuals involved would have been huge. Perhaps they believed in their anti-terrorist cause but no more than an Apple employee proud to build the next version of iTunes.
