I think they are more fault tolerant than that. I run 3 of mine with the side panel off all of the time for quicker access and better cooling.... in a carpeted room. However when changing CPU or replacing thermal grease, I wear a static wrist strap. Isn't it a better idea to leave the power cord plugged in as it's a path to ground for static discharge, if any? Good idea to touch the back of the computer on some non-painted part to discharge any static before reaching inside, however.
For years I would turn off a PC (but not unplug the PC) and change any hardware other than the MB. I now unplug the power cord as PC's still have power to some parts of the MB with the PC turned off. This keeps me from killing a MB if I get a screwdriver in the wrong place. I sometimes still change cooling fans and MB batteries with the PC running.