In order for a jury to impose the death sentence, they would have to think this is the case. If they are unsure, they would not impose the death penalty. In fact, if they are unsure, they are supposed to vote "not guilty" because there is "reasonable doubt".

Some of these "open & shut" cases have turned out to be mistakes. In some cases you have had police corruption where witnesses lied. In some cases you have just had mistaken identity -- someone looks very smiliar to someone else. It happens.

If you remember, a couple of years ago, the conservative Republican governor of Illinois pardoned over all 160 death row inmates in the state and had their sentences changed to life in prison after it was exposed that several past executions were mistakes. Even he realized that there was no way to be 100% sure.