Considering han's fairly casual stroll out of the bar after Greedo's death, I think Han's kind of maybe known to have shot people from time to time... Plus it's a world where everyone walks around with a gun on their hip. I don't think I'd have approached him without my gun drawn either, if collecting a debt.
To that end though, Greedo's just taking Han to Jabba... Han's the one who sort of initiates the threat that, if they want the ship, it's over his dead body... Whether it was over Han's dead body was up to Jabba, but it's over a debt regardless, so I still maintain that Han shooting first is kind of a murder. He owed money, didn't want to pay, and didn't want to face who he owed, so that person sent out people to get him to explain himself. He killed one of them.
Again though, I think it's the world they live in that needs some consideration... It's sort of lawless in that regard. Everyone with a gun on and out, and I doubt Han's credit rating was taking a hit so you either let people steal from you or you physically go get them to settle the matter... *shrugs* It's a pretty fine line.