
"Chips usually have completely separate analog and digital signal grounds"
And also, power supply lines. As an example, ATMega CPUs have an 'AVCC' and a 'VCC'. Same grounds all around, but separate power for analog circuitry and 'the rest of the chip'. Generally, however, proper use of bypass capacitors (etc.) are needed to pass FCC "unintentional radiator" limits on the CPU itself.
There's also proper board layout, use of ground planes [as needed], bypass capacitors located near the devices that generate RF spikes, occasional current limiting resistors on switched signals, and so on.
So I also have to wonder, why wouldn't normal FCC bandwidth and modulation tests NOT pick this up? Or are the 'artefact' signals being generated all within the tolerances allowed by the BT/Wifi/whatever spec?