Confusion with braking-effect of a motor
Yes, it's likely that your motor controller converts the 72V to correctly phased AC drive to drive the motor.
The motor while in motion will have kinetic energy.  In order to slow or stop the motor, that energy has to go somewhere.  You have the choice of burning it off in a resistor, using a mechanical brake, putting it back into the source voltage, or regenerating it into the line.
By adding a large capacitor (yes, on the DC link) you are adding energy storage capability to your source which probably doesn't sink current.  So you can absorb more energy without pumping up your 72V supply to the point where things fail.  You should still have a resistive overvoltage clamp unless you can prove that you have enough capacitance to absorb the worst-case kinetic energy that the system can provide, but this is a more efficient approach than just using a resistor to dissipate the Ek.