I agree with you and I've never got the impression that he killed the half-brother. I can't even think of any reason why he would do so.
I don't think that he did either, but I think that it is sometimes assumed this way because there is a booklet picture with the boy standing over the half-brother with a gun, which lead people to jump to conclusions. But I think this was just a misinterpretation, as the boy certainly isn't evil and probably wouldn't kill the guy who saved him.
A lot of people also seem to think that the half-brother took the bullet for the father somehow. Minor possible detail, but would certainly give extra explaining as to the boy having anger enough to kill his old man.