There were a whole lot of factors that broke down leading up to the Virginia Tech incident; that particular law just wasn't one of them. Why did every single student in every one of his classes know that he was a nutter, but nothing was ever done about it? Why was the administration aware that he'd been writing crazy, quasi-threatening English compositions and scaring the crap out of his professors, but it was a complete surprise to his parents? The problem in this case wasn't that he was able to legally buy a gun; it was that he was a freaking loony, and nobody adequately addressed it, and he decided that he wanted to kill a lot of people.
What do you propose should have been done about it? He was sent to a mental health facility. Part of that commitment should have included a hit on NICS but it wasn't. This bill will fix that in the future.
The reason that the parents didn't know was because the school is not allowed to share any personal info with anybody. Before you start blaming the administration realize that the were following federal privacy laws (Family Educational Rights and Privacy Act). If you have a problem with that law then write your congressman.