Thank you for clearing this up. I would put it this way (in technical terms):
The external power supply eliminates the DC voltage drop in the ground wire of the USB cable, caused by the supply current. This can be a problem, especially because the supply current changes over time.
I would also be very grateful if someone could provide more detailed specifications of these self resetting fuses (something like the description
of their operation and connection diagram). It would be nice to know beforehand, when and why the box will kick me in the face.