Earlier quoted context omitted.
I don't buy that claim. The amount of nuclear contamination in steel is really small. It matters when you're building sensitive instruments, but I don't think nuclear weapons care very much. After all, they contain at least several pounds of radioactive material by necessity. A tiny amount of extra background radiation from the steel casing won't affect things. Adding to my doubt is the article's mention of "pre-1942…
I believe that 1942 refers to https://en.m.wikipedia.org/wiki/Chicago_Pile-1 , the world's first artificial nuclear reactor. Back at the time, there was not very much requirement for nuclear safety/contamination prevention... so if you want steel definitely free from non-natural radiation you'll need 1942 or earlier steel.
Supporting this idea, here's another article on salvaging Japanese wrecks which mentions low-background steel in the context of ships built in 1943 and 1944: https://www.theguardian.com/world/2017/feb/09/images-reveal-...