tldr; The socket didn't properly fit the wrench and they had to manually hold the socket on the end of the wrench. One man dropped the socket, which fell through a small gap between the walkway and missile. The torque wrench was large enough that it would not have slipped through this gap if/when dropped.
If you're dealing with technology so complicated that one person cannot simultaneously design and repair / maintain it, then whoever performs the latter doesn't possess all the knowledge of the former.
Maybe they used an flammable alloy under certain conditions for engineering reasons.
Most metal doesn't burn. But do you want repair / maintenance techs making that assumption?
Multiple by 100,000 parts.
PS: A more realistic example was one of the Skunk Works projects. I forget the details, but either tools of special metallic composition or wooden tools had to be used to avoid damaging the flight characteristics of the aircraft.
Also, it takes an extremely precise sequence of events to cause a nuclear detonation. A nearby explosion is not enough to do it, as you can obviously see here.