If the other situations are safe because other people are around, then the "at home on the computer" is even safer than any of the other situations because *you're* around (you are around, right? if not, why aren't you parenting your kid?)
Your "what if" is just silly:
What happens if they get into an intimate conversation in the hallway?
What happens if they get into an intimate conversation in the classroom?
What happens if they get into an intimate conversation in the teacher's office?
What happens if they get into an intimate conversation on a class trip?
What happens if they get into an intimate conversation if they happen to pass on the street?
If the conversation is inappropriate in one medium, then it is inappropriate in all of them. Besides, if something inappropriate happened to your child, wouldn't you want a record of it that you could take to the proper authorities?
Reducing the contact that teachers have with your children is not, as you seem to believe, a good thing. As a parent, I want my children's teachers as involved as possible. It's a lot easier to learn from someone that you have a good relationship with.
There is a *huge* difference between being a friend on Facebook and spending a weekend together or going shopping together.
That said, there are even cases where "spending the weekend together" is perfectly appropriate. For example, from 1st through 3rd grade, my teacher was also the parent of one of my friends. In 5th and 6th grade my teacher was the parent of another one of my friends. And finally, in 8th grade, my biology and physics teachers were parents of two more of my friends.
Should I have avoided going over to those friends' houses for the weekend because they were also, by definition, my teacher's houses?
I'm so sick of this already... it's one thing to disagree with the procedures, but it's entirely something else to accuse the TSA agents of being a gang of perverted, gay thugs who enjoy groping total strangers.
Oh, so sexually assaulting a stranger is OK, as long as you're not perverted or gay, and you don't enjoy it?
Umm, if the attack from (compromised) AT&T customer machines is causing trouble with AT&T's network, then they should cut off those customers until they clean up their machines. block the people actually causing the problems, not the target of the attack.