So tell me; how can earthing the chassis make a radio unsafe? I'm not trying to be provocative; I want to better understand what is going on with grounding issues.
Very easily
Many older tube amps, had one side of the power cable connected to the chassis sometimes through caps, sometimes not, most used a switch called a polarity switch that was supposed to get rid of any hum if there was some, it also would get rid of the shock you got from the pickups or strings of a guitar, mic, or anything else that might be tied to the un-balanced shielded 600 ohm cable that was also tied to this chassis, installing a 3-wire cord and plug tying the EGC to the chassis, you now have put parallel neutral current on the EGC's, the problem comes when one switches the polarity switch, now you have placed a dead short between the EGC and the hot, to do this you would have to rewire the whole chassis grounding since it is used as one side of the power supply through out the equipment, you would go a lot farther if you would just make sure the plug used is polarized and correctly wired, and the polarity switch defeated.
With that said, back to the OP, as was said, if it is the AM side of the radio having the problem then I doubt very much your going to find much of a way to rid this interference, computers and monitors, power supply's ETC... all produce RF at various frequencies, and AM is so prone to this kind of interference, and back in the 40's and 50's the front ends of these radios were not filtered very well, AM car radios had some of the best filtering, but even then if the interference is on the frequency that is being tuned too, there is nothing you can do to eliminate it, except moving the antenna away from the source, many of these old radios had 4 antenna screws on the back, one for the AM, a ground and 2 for the FM for 300 ohm balance feed line, I have done a 300 ohm balance line feed on stand offs with a twist every 1/4" that helped eliminate some interference then just run a long wire balance di-pole on the roof on stand off's, but if this radio has an internal antenna also without a external/internal switch to defeat it, your still going to get this interference.
I'm not quit sure how you went from being an electrician to a radio technician? but if you have completed your scope of work you need to get paid and he needs to hire a radio technician.