So they do share ground, which is where the interference comes from. You might find sometimes even stereo sound speakers pick up a ticking noise right when you receive a phone call. This is pretty common with speaker systems, wired headphones being a type of speaker system.

Also, a lot of SoCs with FM antennas use the 3.5mm ground as the antenna, so they are wired into the SoC in such a way that they can receive undesired interference.