To develop 0.2 V across 2.7 mOhms requires a current of 74 A, not much current. Ground returns often carry tens of milliamps, and switching-current returns can peak at over 100 mA. Even in a copper plane, moderate currents can cause small voltages that overwhelm typical RF input signals. So, what obliterates a radio signal is unnoticeable in other applications. However, these same currents can cause unintentional radiation from the digital circuit. Fortunately, the same techniques you use to control ground currents in the radio help lower the radiation in digital circuits.
Digital circuits can easily generate large ground-current magnitudes.
The interference that results appears as an increase in the circuit's noise floor. In effect, the noise figure of the radio increases significantly. Ground currents must exist. You cannot eliminate them, so it is useless to try. All current flowing through a node must return so that net charge remains constant.