In the sub being discussed there are 3 wires to main: 2 hot + neutral (I wouldn't call the grounded conductor an egc, as it is intended to carry current and is therefore a "neutral"). If the neutral to the main were to become disconnected, or of high resistance, and someone, for example, switched on a light, there wouldn't be any good return current path. The voltage on the neutral would approach that of the hot that it was connected to through the light and switch. Now, since the egc is bonded to the neutral in the sub, the egc is also pulled up to this "high" voltage. Nice "ground"! So any conductive surfaces that are bonded to this sub's egc (such as the sub's cabinet) are now up at the hot leg's voltage - very dangerous!
However, if you take the same example, except that the egc of the sub is not bonded to neutral at the sub, and instead runs independently back to the main (4 wires to main: 2 hot + neutral + egc), even though the neutral in the sub has the problem of being disconnected from to the main, and being pulled to the hot leg's voltage through the light/switch, the egc is still bonded back to "ground" through the main - preventing the very dangerous situation of having all the subs "grounds" at high voltage.
Now, it is still possible to have a dangerous situation occur even with an independent egc in the sub, but then it requires two faults at the same time - a fault where the neutral is disconnected plus a fault where the egc is disconnected. We hope for only one fault developing at a time, and detecting and fixing the first fault before a one second develops.