I would agree that if the game is predators, running isn't ever going to get you a second shot that you could make.
I have killed several deer, where I spooked or saw deer topping one ridge, and I ran to get a shot at them.
Have ran to cut off elk when I knew where they where going.
If you aren't willing to run when applicable you will limit the shots you will get.
As a side note. You will definately need a tree or be able to get prone, because the chance of you holding the gun still is slim.
This isn't how I sight guns in or anything like that though. When I have guided, it is real hard to get clients to understand that when it is time to go it is time to go. The clients that where in good enough shape, and said ok usually got that second chance I am talking about.
