CatalinaWOW: thanks for the clarification. I think I have a better grasp of how I missunderstood the situation.
1) It is almost certainly illegal for you to make any significant changes/additions to the mains power wiring in any property that you do not own and occupy. Even if you own the fourplex, you likely are not permitted to work on the wiring unless you are a licensed electrical contractor because it is a rental unit occupied by others.
The reason for that is pretty obvious. They don't want ayone making dangerous wiring decisions unless they have some sort of assurance they know what they are doing. Prevents buildings from burning down, killing occupants, etc. Yes, certainly many of us are more familiar with the concepts than many licensed electricians, but we haven't demonstrated that to the local government authorities.
2) Have you actually MEASURED the ground integrity to see if you even have a problem at all?
3) Even if there IS a problem with the green-wire safety grounds for the power outlets, if your test gear (oscilloscope, et.al) is connected to the same outlet as the device under test (DUT), why would there be a problem?
4) Can't you simply use a power strip on your test bench and ensure everything relevant: your test gear, and the DUT, are all plugged into the local power strip. We are assuming that the power strip at least connects all the green-wire safety ground pins together. Whether or not that eventually drains to the crust of the planet is a second-order effect.
1: I would never touch any of the house wiring. I wouldnt even replace a light-switch, let alone futzing around with how the mains ground is setup. Don't worry, I am a "measure twice, then cut" kind of person. I wanted to see if how I understood the situation was correct or not. I now realize that I still have much more to learn before I can fully understand how the negative terminal output and grounding are differentiated in a practical sense.
2: When I test continuity on the ground pins for all of my electrical sockets for one breaker section to another, (Using a Greenlee DM-820) they all return a positive reading. I do not know if this is how it is intended to be or not. I fully admit my ignorance here. I just dont want to blow up my scope if I failed to take precautions.
3: After watching the EEVBlog episode about "how NOT to blow up your scope" (
Link) I just wanted to head off any possibility that I may run into such a situation. I will re-watch it again to see how I got confused.
4: If the dut and scope share the same ground, I was concerned that this would create a voltage feedback and potentially cause damage to the scope or dut. It seemed to me that an obvious fix would be to ground to something else. For example, I have found people grounding out to plumbing instead.