Shaving Upside Down Works?

Whenever I shave, I always have a little tiny bit of stubble left under my nose, and you can see the hair follicles. Recently, I tried shaving from the top of my lip, up to the bottom of my nose, with the razor (it's a Gilette Mach 3 turbo) upside down. This took care of the problem, but I asked my dad, and he said that it leads to the mustache being pushed out and pointing outward to look uglier than before after a period of about a year. Is this true? Because it feels sooo much smoother.