Regardless of what kind of lies we want to tell ourselves, the US criminal justice system is not perfect. Not only do we think that we've executed innocent men, it is well documented. As advancements in modern forensic science are reached, we find new ways to solve crime. With these advances, we have solved crimes and found that we had the wrong guy.
America tends to execute poor, ill-educated members of minority groups. These
members of the underclass cannot afford the expensive lawyers who often get
more successful members of society off. Frequently those who are executed
have severe mental troubles, and cannot even help much in their own defense.
Almost certainly, America has executed men and women whose only crimes
were being poor, ignorant, and perhaps a little crazy.
I think you would have to say it would be almost impossible for the US not to have executed innocent people in the past. We have a good legal system but it is not perfect. There are going to be times we get it wrong because it is in the hands of people.
Yes, It is possible that someone could have a lot of evidence be aimed at them for a major crime, and simply be in the wrong place at the wrong time, but still be proven guilty in a court of law. Once guilty, if the crime was bad enough they could be executed.
Yes it is certainly possible that the U.S has executed innocent people. Let's not forget that as much as the U.S criminal justice system has improved in recent times it is still a man made system and as human we are inherently flawed and biased. Another thing to consider is the fact that the inclusion of DNA testing in the criminal prosecution process happened quite recently which means back in the old days the evidence collection tools we have today hadn't been included in the process