Unfortunately it seems your board has a short. (I am assuming that you measured the power to ground of the Galileo board not the power supply?)
I would doubt that the USB cable is the cause of the short. Most likely it is a manufacturing defect. Sorry, that your board has that problem, but every mass produced electric device is bound to have some products with defects.
The good news is this is the only case I have heard about, so if you get another Galileo it is not very likely to have this problem. 
