I'm not a metallurgist, but I did take a class at MIT on the subject and worked in a metallurgy lab for a couple of summers. The temperature of steel has an effect on the nature of fractures that can occur. Ductile fractures start at a crack and the steel deforms as the crack widens. This is the way most everyday metals under everyday circumstances act. The deformation absorbs energy and dissipates the forces acting on the metal. If this occurred in a beam, it might be observed to be deformed before a catastrophic failure happens.
Brittle fracture is different. A crack forms and it travels rapidly like breaking glass. Such fractures travel through the metal at the speed of sound through the metal (over 2000 ft/sec for steel). Pipelines in Alaska can experience such fractures. Such a fracture could travel thousands of feet because at the point of fracture there is no pressure drop at all (since that drop in pressure would travel at the slower speed of sound though natural gas).
This is a concern in Alaska because a piece of steel can exhibit ductile fracture behavior at ordinary temperature but transition to brittle fracture at lower temperatures. This transition point depends on the steel composition and its history. The history of the steel includes heat and mechanical treatments during it's production, but also the stresses put on it during its use such as welding, shaping and forming, vibration, and even exposure to radiation (which will occur in some parts of a submarine since they contain nuclear reactors). I have no idea how the steel was intended to be used, but conceivably there could be good reasons for the -100F requirement even if the steel was never going to come close to this temperature. (For example, I know nothing of the relationship of radiation embrittlement and the ductile-brittle fracture temperature transition.) So while the testing requirement sounds "stupid" it is perhaps even stupider to ignore it.