I would never put my bike upside down. I hold it up by the seat or seat tube to get the rear wheel out. Then, I lay it on the left side while I am working on the tire.
Besides putting pressure/damaging the bars and other stuff, when the bike is upside down, everything I have to do and look at is backwards, which for me is death. My visual perception and ability to remember what to do is limited at best, and I need things to be exactly the same every time!