You are incorrect about one thing. You said that turning left or right to the instructor is different for the person learning who is standing on the other side of the component. This is not true. Try it. Stand on one side of a component and do lefty-loosy…then go to the other side and do the same thing…..you’ll notice that the screw is still coming lose and not getting tight.
The same goes for clockwise and counter-clockwise. If you stand on one side of the component and turn a screw clockwise and then go to the other side and turn the screw clock wise, the screw will still be getting tighter.

So, you’re logic fails on that point. You are correct about the point that you’re not really turning the screw to the right or left, but people don’t generally think like that. Just like with cars…you’re not really steering left or right, you’re steering clockwise or counter-clockwise. But we’ve used left and right for so long that our brains automatically know what to do.