But you're right in that if I was actually working on the 787, I would have no such faith, and would verify the designs I was responsible for.

In 1989, a DC-10 operating United flight 232 suffered an uncontained engine failure which damaged the tail and disabled flight controls, resulting in 111 deaths (and could have been more, but in a freak of chance, a DC-10 flight instructor was on board and was able to assist the crew in landing, which may have made the difference for the other 185 people on board). In 2010, an Airbus A380 operating Qantas flight 32 suffered an uncontained engine failure which damaged a wing, disabled a hydraulic system and braking systems, and disabled some flight controls while starting a fire. It resulted in... zero deaths.

In the early 1990s, Boeing 737-200 and 737-300 aircraft had a variety of uncommanded rudder movement issues, resulting in at least 157 deaths. In 2012-2013, the 787's battery fires resulted in... zero deaths.

In other words, the main difference between "then" and "now" is exactly the opposite of the usual arguments against modern aircraft development: more recent aircraft, when they have serious issues, result in fewer injuries and deaths than older aircraft when they experienced serious issues.

This track record of improvement gives justifiable faith that modern aircraft development is safer.

There was an in-flight fire, on an ANA 787. It made an emergency landing and the plane was evacuated. No lives were lost, and the airframe was not lost.