I remember reading that 'some scientists' believed that a nuclear explosion could ignite the atmosphere (chain reaction of atomic explosions) and wipe out the whole planet. I'd like to believe that, being rational men, scientists would have disproved the possibility long before performing an experiment with such catastrophic contingency and high school textbooks only include the reference to further dramatize the nuclear testing. (Not sure if this is a better question for AskHistorians or AskScience, so XPosting it.)
The idea was floated briefly in 1942 or so but it was not very hard to calculate that even with really optimistic assumptions about how such a reaction would propagate in the atmosphere, it would still cool down too fast to be of any consequence. There are just too many nuclear processes that can sap away energy, and you need a LOT of confined energy to create large-scale fusion reactions.
If you are curious about the science in question, it later got written up as a report. Basically it was easy to calculate that the N+N fusion reaction was not easy to get started and even if a few reactions did occur it would not be sufficiently hot to maintain further reactions. It turns out it is very hard to make fusion reactions work on a large scale and they knew this during World War II, well before the Trinity test. It proved to be one of the most difficult parts about solving the problem of the hydrogen bomb (which was explored during WWII as well) — not only will the atmosphere not easily ignite, but even if you want the fusion fuel to ignite, it's not easy for that to happen either.