Fast logic signals can quite easily cause a large voltage drop across that little ground clip.
The world becomes very interesting when you consider "when is a ground not a ground", which for AC signals, is all the time. Think what will happen if the ground clip is a relatively large impedance (like 100 ohms), and the probe-to-clip (at the coaxial tip) is a similar impedance (1000 ohms or so), and the impedance from ground clip to oscilloscope frame (i.e., the probe cable's outer shield impedance) varies between, say, 10 and 1000 ohms depending on frequency (because it's a transmission line and an antenna, being a wire through space).
Just for hand-waving's sake, you can imagine these impedances as resistances, and see how all the voltages and currents differ from the naive DC case. In reality, they are of course impedances, that interact to create peaks and valleys as L and C resonate together, but for a qualitative illustration, resistors will suffice.
Tim