1 wire absolutely does feed the radio and provide the memory for the radio. I am an MECP certified installer and this is a very simple setup that pretty much every vehicle on the road uses, at least before the data controlled radios showed up. If there are 2 BATT wires coming to the radio, as the photo above suggests, this is simply to provide sufficient power to the radio. BATT and MEMORY are the same thing. It is just one wire that has battery voltage at all times.
The BATT wire has battery voltage all the time. This wire literally comes from the battery, to the fuse box, and then to the radio. This provides the memory to the radio, and the power supply when the radio is turned on. There is no way to switch this on or off. It is straight battery voltage.
The ACC wire is the switched wire that turns the radio on or off when you turn your key on or off. This is basically a TRIGGER wire. When the radio sees 12 volts on this wire, an internal relay trips and turns the radio on. It is now pulling power directly from the BATT wire in order to run the radio. When you turn your key off, it loses voltage on the ACC wire and the internal relay stops pulling power from the BATT wire to power the radio, but obviously the BATT wire still has 12v. This is what provides the radio's memory. This is also why, usually the ACC wire is a thinner gauge wire than the BATT wire. Because it doesn't carry any amperage, the BATT wire does.
I believe you are over thinking this. MEMORY is a wire that would be 12 volts at all times. BATT is a wire that is 12 volts at all times. And the BATT wire is the one that actually powers the radio. The ACC wire is a trigger, that's it. It does not power the radio. BATT does.