So that would mean that if I have a 100mA load I'm going to get a totally different voltage than I would I I have a 4A load. That's not what I've experienced in practice. The voltage generally remains the same unless something with a massive amp draw is running.
Theoretically, the voltage at the green points is 12V. Practically - it can't be measured without disrupting the system because we have to use some kind of instrument.
We had the Fluke version of the differential voltmeter in my lab at TI in the 60s. I don't think they have changed much in theory since then.