Using the facts we know and filling in the suppositions in a way different than the article tries to force the portrayal we can easily get to a place where this is self defense.   Everyone in this thread seems to be assuming these events happen in immediate succession.  Homeless guy gets up bangs on car window, she says she has a gun, gets out of the car shoots at him twice, gets back in car drives off.   Say 30 seconds to 5 minutes elapsed time.   Now same facts but with different timing homeless guy gets up bangs on SUV she says she has a gun he leaves, 25 minutes to an hour pass.  She gets out of car to go to a restroom or to get food or simply to stretch her legs,  he sees her out of the car and attacks her.  She shoots twice runs to SUV and speeds off.  

Same basic facts as provided in the article with two very different 'outcomes'.