The description of the cable on the e-bay store is really weird.
It is a non standard cable, but you reported it works well with some of your phones, when connected to the due's native port. From this I deduce the ID pin inside the micro B plug is connected to ground making it actually a working micro A plug but with the wrong B (trapezium) shape.
Because of the wrong shape you can also insert it into the programming port. But the latter ignores completely the ID pin. So this makes you connected two usb devices. Nothing should happen in this case, it should cause no harm, but you are right that neither of the devices should source power.