According to BL-36 the BCM terminal 58 supplies power to the back door latch actuator (no. 13 on page 173) so yes the BCM is a factor, but may not be the culprit. You should diagnose the electric latches first.
Have another look at BL-173 and 174. If or when you can manage to unlatch it and keep it open try to access the motor and unplug it first so it wont try to close the door when the button is pushed the second time. With the motor out of the way you can test for power going to the latches (the ones in right side box on p. 173). Test for power on the latches with someone else being the button pusher. You should get power on all those latch harnesses. If not you should check terminal 58 of the BCM (orange wire). If that works there’s a break somewhere between the BCM and the wires going to the latches. If that’s not the problem check the mechanical movements of the latches before you condemn the BCM. BL-39 and 40 talk about checking the bcm power supply. Pay attention to no. 2 and 3.