You might have an intermittent fusible link (or connection) at the positive battery terminal. Hook everything up and wiggle the cables. When you check the battery voltage, do so with some load on the battery (dome light, headlights, etc.). A high impedance voltmeter can measure 'normal' battery voltages through a high resistance connection.
I'm thinking if he measured from "battery terminal" to engine block, he'd actually be measuring from the bolt that holds the terminal to the battery. If there was any significant resistance between the battery and the cable, it would mean the bolt wasn't helping any, because the bolt touches metal on the cable end; the resistance would be between battery and bolt as well as between battery and cable. So if he could get to the actual battery terminal, he'd measure a higher voltage than at the cable end, because there'd be a drop from the 20 mA draw through that connection resistance. But he probably wouldn't be able to do that.
I know I put the resistor elsewhere, for simplicity, but for the practical discussion you've led me into, he probably still would not see any drop, it would already be inherent in the measurement. With the resistor where I originally specified it, it would be easy to detect the voltage drop, as you suggest.
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