You said emphatically that his story was BS - that implies a fair degree of certainty. As for your other point, both people probably do say the other guy started it but I don't agree they both believe it - usually one of them is lying to avoid getting in trouble.
Looking at the map and reading the transcript of the call, it's not hard to see how his story makes sense. I was mistaken that he got out of his car just to look for an address - he was also following Martin on foot, but that doesn't make him a criminal or even indicate he was looking to confront him. He followed Martin through what he called a "pass through" (the space between buildings, probably an easement) and lost sight of him. The cop tells him he doesn't need to follow him and Zimmerman says OK. He then tells the operator he doesn't know exactly where he is because he's on the sidewalk between houses (he's not chasing him through back yards) and can't see an address. So instead of giving an exact address, he directs the operator to tell the police to meet him at a particular spot. So is it so hard to believe that as he's walking back to his car to go and meet the police, Martin surprises him, starts beating the crap out of him and as Zimmerman said, tells him "you're gonna die tonight"? Considering the only injury Martin suffered was the gun shot and scratches on his knuckles (indicating he was striking Zimmerman and probably struck the ground) - he doesn't have scratches on his head or body, no bruises or any defensive wounds indicating Zimmerman assaulted him and the fact Zimmerman passed 2 lie detectors, it seems more than likely he's telling the truth.