The bill to ban armor piercing bullets was poorly written. They were using the bill to ban small calibre rounds, yet larger calibre or high-velocity rounds will pierce your basic body armor back then just as easy.
In addition, there was no clear definition within the bill if this "ban" extended to military applications. If our rounds, even small calibre, cannot penatrate an enemy's armor, then we are in trouble.
However, if you read the clearer sections of the bill, it was also calling for the bans on rounds that would penetrate softer body armor, such as flak jackets. Most hand gun rounds can penatrate flak jackets at close ranges.
This was more of a PR bill than anything. If you want some good information regarding protective vests, I recommend:
http://www.nationmaster.com/encyclopedia/Bulletproof-vestIt discusses the urban legend of "cop killers" back in the 80's.
