Actually that is not strictly correct, you want it connected to the
machine you are working on. If the strap is simply connected to ground
and the PC is on a plastic picnic table the PC could have built up a
static charge that will kill chips when you touch them. In fact it does
not matter if you have a static charge of a million volts as long as you
are at the same potential as the PC,,, usually achieved by touching the
case.
First is the easiest - Since the components are isolated from the
case there is still a "million" volt potential between case, you, and
the motherboard. Unless, of course you are trying to tell us all
that the motherboard and all component leads are attached to the case
and reach the same potential. In other words, the "PC" as you
quaintly call it is more than just one thing - A metal case and a lot
of components ---not--- at the same potential as the metal container.
Second, the obvious you neglect - Not to mention the fact that if you
are connected to ground you will still bleed off the charge of
yourself and metal case to ground potential. No million volts.
Thirdly - Your scenerio gets even more ridiculous because if the case
on a plastic table builds up a huge charge and you connect yourself
to that charge and touch the ---isolated--- motherbaord, guess what
happens!?