Nomad
Master Black Belt
They put a lot of sacrifice into their training, by putting aside their family and anything else that may distract it. They constantly diet and lose weight before fights/competition. They often lose out on family time and social events. Why? Because to them - there is nothing as important as winning.
To me, this is the key sentence in this argument. In order to be "the best" (if that's possible, since genetics undoubtedly plays a role (e.g. Michael Phelps - size 14 feet and double-jointed ankles!)), you have to make a choice to effectively eschew many other aspects of what I'd consider a balanced life. This includes personal and familial relationships, work (until you're good enough to make your competitive sport your job at least), and social activities.
Now, I'm thinking. Are those who say it is not important, doing so because they've never been good at competition? - Perhaps it's the, how can something I'm not very good at be important to me, mentality? Maybe fear of the unknown and/or failure, so I won't even compete, to keep myself from failing? I don't know, but sometimes it seems as though, the folks saying that "winning is unimportant" - probably didn't win very often, some may have never won at all.
When I started martial arts, I was much more competitive than I am now, and I was pretty good at it and have a few boxes of trophies to show for it.
The change away from competition came from a few things. One was tearing my ACL and having to undergo the long road to recovery following that. Another was the accompanying realization that while the 20 year olds were somehow staying 20 (or being replaced by new 20 year olds), I wasn't anymore, and had definitely passed my prime. A third was looking at the lack of attention that other things, like my family and my work, were getting while I was in this uber-competitive mode. The focus of my interest in martial arts started to shift away from competition towards more self-defense applications. Altogether, the plastic trophies weren't worth the cost (in terms of health, money, lost time with family & friends, etc) to me.