Buffalo,

If you leave the machine plugged in and just turn the switch on the PSU to
OFF,

That might once have been be good advice, but not so much nowerdays.

These days computers can be "off" but still have parts of it powered so
that, for example, pressing a certain (or any) key on the (USB!) keyboard
will boot it.

Some motherboards have a LED to show its still (partially) powered even when
supposedly being off, but not all.

Pulling the powercord and waiting for a minute or so (to give the capacitors
in the power supply a chance to drain themselves) is the best way to go.
With, or without actual grounding.

So, just touch a metal part of the machine before touching any electronic
part and both will be at the same potential.

And that will be true even with power cable (and its grounding) removed. :-)

Regards,
Rudy Wieser