As anyone can see by the responses to these threads, there is good chance that a person who would be on his jury may choose to believe Zimmerman. No doubt about it. And while prosecutors do NOT need to "prove" the story must be false, they will presumably do their best to do exactly that, with anything that would contradict it--anything at all. They will also presumably do their best to show that he is inclined to lie. They'll try to make it as difficult as possible for a person to accept his word.
And to those who would be inclined to deny his story, because there are plenty of those people, too, the prosecutor will take them down a timeline of sorts, asking them to logically put the events together. The fact that Zimmerman overwhelmingly desired to have this person questioned, the fact that he was known to have directed himself toward Martin, the fact that such activity would logically place him into the immediate vicinity of a person whom it has been said was physically superior to Zimmerman. The net result being a situation to cause both individuals to become fearful for their lives.
Please remember the definition of the charge, which is a creation of an imminently dangerous situation while revealing a disregard for life. (In other words, being an impulsive dipstick will absolutely qualify - with NO premeditation, as some are convinced must be true).