So I think I understand it:
If the scope and the Device under test have the same reference ground, you don't need to use the scope probes earth lead.
...<snip>...
That is only true for DC and low frequencies. If you are probing high frequency signals, then the length of the ground connection can make a big difference. This is why the ground wire is brought out at the probe end of the probe's cable. And why a short wire is used from there, and often the simple spring wire connection which is pressed into a ground connection on the PCB within millimeters of the point where the signal is being probed.
Generally speaking, the upper end of audio frequencies is about the limit for not using the probe's ground connection.
AND
...<snip>...
As I (hopefully) understand it, the biggest problem is connecting the scopes earth lead, on the device under test, to something that is thought to be ground, but is in fact some (high) voltage? And Zap/bang/smoke.
...<snip>...
That is exactly correct. You do not want to accidentally ground a point in the circuit that is not at ground potential or that can not be forced to it (as in a device powered by a battery or a floating power supply). Professional, well designed PCBs will have numerous ground points clearly marked at various, needed points around the board. Generally speaking, it is safe to connect a scope's ground clip to any one of these.
If the PCB is not designed and built to that level of professionalism, then you need to be extra careful. This would be a good place to use a good quality VOM, starting with the highest Voltage setting if it is not auto-ranging.
AND
As for touching things with your hands, TURN THE POWER OFF FIRST and WAIT A MINUTE OR TWO for the caps to discharge.