A correlation between the robbery and the shooting is only relevant to the cop's state of mind. If he thought Brown had just committed a robbery (and was therefore possibly armed) in addition to attacking him, it provides greater justification for shooting him, even if he was trying to escape. If the cop did not stop Brown on suspicion of the shooting, he can't provide this excuse.
However, Brown's thuggish conduct just minutes does provide evidence that was an aggressor who initiated the fight with the cop.
Also, is anyone else's mind just blown that edna is more deferential to the cop in this case than I am?