Thanks LuvsJack...
You know, I think that we are all closer than we think in this situation.
Most of you know, as I stated earlier, I have a huge problem when schools usurp the rights/responsibility and think they should become overinvolved. Believe me, I do NOT see the school as having any overriding mandate to monitor or police activity outside of school. NO WAY!!!!
Remember, we are not talking only about this one particular case. (Further reading does show that the school did make some effort.

) To be honest, what was quoted in the OP might be misleading, as it seems to state that the school just blew-off the parents.
I am looking at the main issues here... The question, as asked in the thread's title.
I will try, once again, in a very simple way to state just where the school's responsibility begins.... When the parent's, themselves, present credible information that there is a case of physical threat or serious sexual harassment being carried out by a student/classmate..... Yes, at THAT point, I think the school does have a responsibility. No question.
It appears that,
in this particular case, the school did make an effort to look into it. They found their hands tied, with insufficient evidence to determine that the boy in question was involved... (like the Principal said... 'Yeah, right....'.) But, they did acknowledge the problem and make a reasonable effort. So, in this individual case, I might possibly feel that the school did make an effort to meet their responsibility.
If the parents wanted a lot more than that, I think it was just desperation and wishful thinking. Like many have said, if you are wanting the schools to have too much authority - Better be careful what you ask for!
Personally, I agree, totally, with the feelings/views of the one Principal quoted... He states that he simply doesn't see why kids at younger ages should have free reign of these technologies. Of course, I would very very STRONGLY disagree that an educator had any right or authority to make that determination for families... But, I do have to admit that I agree with his views.
I suppose I just have a problem with reasonable, concerned, parents being attacked and Parent Bashed.