Earlier quoted context omitted.
At CERN, the previous accelerator was the LEP. Story goes that when it was constructed and first turned on, it was shutting down due to beam not stable. They found out that someone put a glass bottle of beer right inside one of the beams tube. And the detector of Alice at today's LHC was built using steel by melting down old Soviet tanks.
I'm presuming that the tanks were a source of low-emissivity steel?
My guess: low background steel is demanded more by low-background experiments like neutrino or dark matter detectors. Most of the LHC experiments work in an environment with enough (intentional) radiation to require special radiation hard electronics. The kind of environment is orders of magnitude more radioactive than the ones where the background radiation from steel becomes important.
But please correct me if I'm wrong!