That's a good question, especially when it comes to 9/11, because relatively few of us were materially affected by what happened that day (assuming you don't count trickle-down events like unemployment, war, and such). In a bit of irony contrary to the "never forget" meme on the Internet, which is like suggesting you could forget someone cutting off your arm, I read a blog post yesterday by a woman who was a block away from the World Trade Center when it came down, and she's spent the last decade trying to forget what she saw that day.
Something like a terrorist attack that killed thousands of people certainly can stir a bit of empathy, but like the woman who was there, it's not likely we can see it the same way via our TV's. There are a range of other things we encounter electronically as well. For example, a friend had a baby yesterday, and while there are happy moments captured in photos on Facebook, it's certainly not the same as being there.
This begs the question, does our electronic connection to people and events cheapen our lives? My take is that, like so many other things in life, it's not a binary condition. Unless we never leave our houses and interact with others, it's not that these connections lessen the value of our lives. Instead, these connections simply add to our lives, not replace those that are front and center, in the flesh. I think it's a valid point that these connections are different, and most are not as intense or personal as those in "real life," but it doesn't mean they're cheapening the whole of our experience.