I was bullied in school as well (though not to the extent that these children were bullied,, and I saw other kids receive much worse treatment than I did) and from my experience the problem is that the "bullies" aren't the stereotypical big, tough, mean kids - they are the polite, well-like popular, extroverted, generally good-looking kids.
So when an incident comes to the attention of a teacher or other school authority - who is only human - they tend to take the side of the nice, popular kids, who they like anyway, and blame the kid who was bullied for somehow causing the incident to happen.
In my years in school - I graduated high school over 25 years ago, so things may have changed - I don't think I ever saw or heard of a child being reprimanded, or even scolded, for bullying someone else.
Children got punished for getting into fights, but not for bullying.