While the Challenger crew were the first to die during a mission, they were not the first NASA crew to be killed. The three-man crew of Apollo 204 (aka, Apollo 1), Gus Grissom, Roger B. Chaffee and Edward H. White II were killed in a fire in their capsule during a launch practice run on the launch pad on January 27, 1967. The docuseries makes no mention of this earlier fatality (what the NASA engineer said was that no NASA astronaut had been "killed on their way to space" to fit the narrative of the Challenger deaths, so it was a matter of semantics).
At a point of the third episode, it is told that due to the letters that Christa McAuliffe was writing in her leisure while she was training for the Challenger, McAuliffe joked nicknaming the mission "The Write Stuff", in allusion to the movie The Right Stuff (1983).