I voted no because while it can and does happen, it does not always happen.
I can only thing of three PC on PC fights in the games I've been in over the years. One was in a cyberpunk (genre, not system) game where my mercenary and another player's bodyguard got into a (quite potentially lethal, considering their unarmed skills and augmentations) brawl. This was do to differing personalities of the characters. Essentially the bodyguard was cynical, paranoid, aging, came from nothing, and was slowing down and starting to miss steps. My character was young, reasonably successful, had a relatively normal upbringing, and was idealistic. It was basically a challenge over who the alpha was.
The other two were in an oWoD game. One was a fight between my Akashic and a Thrashing Dragon who was strung out on gold chi, and the other(s) don't really count since they were jiyu kumite (free sparring) between my character and his student. Both were quite potentially lethal, the former much more so then the later.