We're almost saying the same thing. However the current from a wall wart charger is mainly determined by the internal resistance of the CHARGER not any battery connected to it, as Rodney says.

However if you take a wall wart apart you'll find that it's not the windings of the transformer which are the major part of the internal resistance it's the resistor stuck in series with the transformer. It's placed in there specifically to define the output current, a sort of poor mans constant current device.

But you're absolutely correct about one thing. If you want to KNOW what's happening measure it, don't just guess

Steve