static electricity is discharged from your body when you touch metallic parts. That being said, even if you have the psu plugged into the wall to have good ground wont help if you have a lot of statics in your body. The electricity will probably just jump to the sensitive circuit if you happen to touch them before touching any metallic parts. When you open the case, you already grounded yourself because you already touched the case and the panel and keeping a hand touching the case while working in (if you can) will help to minimize the risk. I always try to keep a hand touching the case while verifying connectors, wire,.. If I have to remove one component and need my two hand then I touch the case with one, then touch the part I have to remove with the other then remove my hand from the case and remove my part. Be sure to drop it on non conductive surface because, on extreme case, static can build up very fast and touching something conductive with the parts will have the electricity to jump from you to the part to the conductive surface, which will be bad. Same thing when you have to pick up a part to put in the case. Ground yourself, pickup the part, ground yourself again before removing your hand from the part.
Static is not really electricity. It is a phenomen that happen when the protons and electrons are not in equal number. When you rub your hand to some surfaces, such as rubbers, or walk on carpet, you are loosing protons and you end up being charged with more electrons than protons. touching something conductive just balance back the thing.
-Always put the blame on you first, then on the hardware !!!