They knew that in stars common elements of the earth’s atmosphere (like hydrogen, oxygen & nitrogen) will combine into other elements, releasing huge amounts of energy in the process. The fear was that a nuclear bomb would spark the same kind of reaction in the earth’s atmosphere.
They did calculations, and decided that even if some nuclear fusion did occur, the energy lost would outstrip the energy gained, and there would be no runaway reaction. The exact mechanisms require a decent level of understanding of nuclear physics (which I don’t have at the moment).
The risk didn’t increase, because it was never a real possibility. The “risk” was that their understanding of the science wasn’t correct or they missed something (like the unexpected reaction of Lithium-7 during the Castle Bravo test).
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