If a non-radio device is picking up radio signals it can never be the Transmitter which is at fault.
It must be RF breakthrough caused by bad (eg cheap) design in the device.
Source: Retired EMC engineer.
P.S. I've never heard of people building an AM radio with a wire and a tin can. And if it were possible, any fault would be with the poor receiver not the transmitter.
(Capacitor can be made out of foil and paper, crystal out of the graphite from a pencil and a razor blade. The radio pioneers were pretty inventive. Google early crystal radio receivers.)
"..any fault would be with the poor receiver .." is correct, but if you took the time to build your own crystal set, definitely go see the ham next door, he most likely has the parts in his component stash to add some better RF selection/rejection to your radio.
Just like most of you like to tinker with code, we like to tinker with radios.