Ever look around in today's world? In mean, seriously, have you watched the news lately? This is the way the world works and learning this is also a valuable lesson. Ignoring it isn't going to make this problem go away.
Yes, when you allow bullying to go on, you're ignoring the problem. I'm advocating that we deal with the problem head-on, at the kindergarten level, before it becomes ingrained. One way to make the world a better place is to make a conscious effort to teach children how to deal civilly with their interpersonal conflicts. Some kids are able to figure this out by themselves, but there are a few in every classroom that need help.
Look at any business environment where people are even remotely ambitious. Think there's going to be back-stabing going on? Think there's going to be people who don't care either way? And that's where most of the world works. Hell this is even true to some extent in academic circles.
And see how productive these poisonous, backstabbing environments are! I used to work with a guy who kept trying to copy and take credit for my work, because he was underqualified for the job and was scared. Everybody used to laugh at him on the side because he was such a useless and awkward guy... had all sorts of mean and childish nicknames for him. We could have continued the situation where our boss would have gotten half the work out of us because my coworker was always trying to make himself look good at the expense of productivity. Instead, I had a firm but friendly talk with my coworker, discussed how we should divide the work, promised to help him a little, and didn't laugh at him. After that, though things weren't perfect (he still had issues with other coworkers), they were a lot better between us at least... and we spent a lot less energy on conflict and competition, and more energy on actually getting experiments to work.