I encountered a negative power supply for a TV in a magazine a few years ago. The author was going on about new technology and varying the effective size of a capacitor to control regulation. All you had to do is flip the schematic over and put the ground symbol on the output and the output symbol on the ground connection to see that it was nothing but a standard positive regulator operating into one of your holes.
I didn't think anything was special about it at the time, but I just looked in my notebooks and found that I did that 13 years ago. It never crossed my mind that someone would find that unusual.
No matter how you “twist-it", or where you declare your reference to be, in the end it still comes down to relative potentials, so nothing will change. There’s no such thing as “positive or negative” alone, it’s only in reference to some other potencial that makes it either + or-.