Non-ionizing radiation can cause chemical reactions (photochemical, heating, burns) that damage cells and might lead to increased cancer risk.
I really doubt if that is the case with mobile phones but I think it makes more sense to look at the epidemiological data rather than make a bunch of hand wavey arguments about the radiation. There are a hell of a lot of cell phone users and if there is a risk worth being concerned about I think it should have shown up before now.
The negative effects are widely believed to have been caused by a 750W radar jammer, which frequently radiated the ship deck. There hasn't been established a clear cause-and-effect link.
Short of some indication that they were turning on the jammer all the time in the workshop I would sort of think chemical exposure would be a more likely explanation.