I've got an old solid state RCA Victor wooden table top AM/FM radio with a metal sleeve on the power cord, similar to what Chad mentions. Except this is external and I can disconnect it from the antenna terminal. It works fine only if the signal is strong.
I also have some old B&W portable TVs that have the same setup for the built in UHF antenna. There is no direct connection to the AC power line, just like the RCA radio.