They think they do, and they have this idea because for them there is no correlation between justice and executing the person who actually killed the police officer. The system to them and the sentence of death is about vengeance. Those people do believe in an 'eye for an eye', but they don't care about which particular eyes are involved in the equation.(I am not going to argue the morality of the DP here. I don't believe it is moral, but that is a different discussion than this one.)
You can argue all you want with them about the lack of evidence and recantations of statements. That isn't the point to them. Officer McPhail was gunned down in cold blood by someone of color. Troy Davis was involved by being in the same area code when the event occurred, and because he was a person of color with a rap sheet. The facts that someone of dubious character mentioned his name, he was obviously a triflin' person up to no good, and that Davis was not someone who had powerful connections made him a perfect fit.
In this case and others, the system uses "The Neighborhood Play' from baseball as a guide. When a double play is turned in baseball, second base has to actually be touched for a force out to count. However, if the fielder is in the neighborhood of the base during the play, it will still be ruled an out by custom in many cases. Troy Davis was in the metaphorical neighborhood so why bother with being exact and adhering to the letter of the law? If it's good enough for baseball.............
People don't see individuals. Instead they see groups of interchangeable parts. That has been a major societal problem for years, and it is getting worse. If a Congressmook knows of ONE example of theft, fraud, or cheating in a program such as unemployment benefits, that one person becomes the standard by which the entire program is judged. That view is then passed on to people who are predisposed to believe it anyway, and voila! Unemployment benefits need to be cut because it's used only by frauds.
This reasoning is pervasive and unfortunately has deadly consequences. People who wanted Troy Davis executed no matter what other information was presented are sitting smugly in their moral certainty because he was in the neighborhood and close enough to their idea of someone who would be involved. People of color are seen as a monolithic entity too many people.
Todd Willingham who was executed by Texas for arson and the deaths of his daughters was caught in the same neighborhood trap. He didn't have the added burden of being a person of color caught in the system, but he was poor and did have a rap sheet. To Perry and others, so what if he didn't really do it. He was a drag on their view of society so it was no loss to them. The Memphis Three were lucky to have been freed. They also fit the neighborhood ideal as suspects. Damn any facts!
If you are caught in the system and perceived as "an other" who is outside the circle of those people seen as acceptable by the PTB, you might as well start gnawing your foot off at the start. You will be lucky if you escape with just the loss of a foot if you escape at all.