There is video of Brown's aggressive threat to others just prior to the incident that cost him his life. He wasn't shot because of petty theft. He had just victimized a business and a person with violent behavior.
Experience with violent people, especially if they get by with initial aggressiveness, demonstrates that they will generally increase their violence until they are stopped by an outside force so, in defense of the jury, it is not difficult to believe that Brown had quickly become even more violent.
At first thought, a leg may seem a long way from a head, but thinking through the possible scenarios--a larger man advancing on a smaller man holding a gun who's hands go up in defense or a larger man pushing/ grabbing the man with the gun--the shot could hit the aggressor anywhere. A policeman is trained to manage the situation in the safest way possible, but variables mean bigger risks to everyone, especially a criminal.
If a policeman tells a person to stop their advance and the person continues moving in any direction, the spot they will get shot in is undeterminable beforehand. The aggressor may jump, drop, plunge forward, or fall backwards as he attacks.
The media's handling of this directly contributes to the continuing violence and it is a shame that we are tolerating it. It is very sad that the people in that city have been influenced by the media's response to the decision of the grand jury.
The media could be helping the situation but they are inflaming it. The people there, with the right guidance, could pursue intelligent and productive avenues to highlight the issues. It's heartbreaking that they are choosing to destroy their own community and teach their younger people to self-destruct.