Did you try to slightly increase rpm of the good car by pushing down the accelerator pedal a tiny bit? Increase rpm to about 2000 before trying to start the engine? Last time I tried to jump start a car, the engine of the good car was audible having trouble running stationary. Starting a car requires substantial amounts of energy.
Good quality jumper cables and clamps can make a difference too as they bring low resistance. You are essentially loading the known good vehicle with a large charge current for the battery and a large starting current for the motor. Cheap, thin (often aluminum rather than copper) wires and poor clamps will not only heat up, with that they'll also drop the power available to the starting vehicle substantially. Think order magnitude in excess of 100 Ampère to start the engine.
And yes if the battery is still able to charge and discharge at a substantial current, which is often the case if it hasn't been too long at low voltage, then indeed the low battery impedance will help a lot. Here is a video on YouTube where a battery is charged from penlights. https://www.electroboom.com/?p=602