1 single 4.2v (Fully Charged) lithium battery will supply max brightness (in the flashlight world they say "direct drive", most would say a short i guess lol)
This is simply because the output impedance of the battery limits the current drawn. This would not necessarily apply to any voltage source of 4.2V.
I think this is what the OP is seeing when he says that the figures do not add up. By not taking into account the supplies output impedance you get a false idea of the current you can draw.
It is not that simple either. The output impedance changes with the current draw, that is it is not a linear impedance, which is why the graph of voltage against current is not a straight line.
The voltage out of the power supply has no relevance here.
Apart for setting the maximum voltage output of the constant current driver (minus a bit for the drop across the driver's internal components) .
Some of us remember the constant current output of mechanical teleprinters. They outputted a 20mA constant current into the next teleprinter. If this was a few feet away the voltage needed to drive this current was small. But they could be connected at a distance of a few miles apart, this required a much bigger voltage. The ultimate was when it was disconnected so it never stood a chance of driving 20mA then it could output 180V, enough for you to get a bit of a shock from, but connected up it had a very low voltage on the terminals.