Don't see where this would matter if the person was right or left handed. If that were the case then one side should read up & the other side down. The inverted side would be opposite for the left hander from a right hander.
Anyone ever seen gune with the writing inverted on One side, I haven't, course many of you have looked at a lot more guns than me.
I will say that when I want to look at the writing or engraving on the "Off" side of a gun I normally turn it around, not over.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra