You are correct. In a criminal case, the burden of proof is BEYOND a reasonable doubt.
Meaning, there can't be just a doubt. It is a standard that goes BEYOND that. It's the highest burden of proof there is, which is imporant in any case, especially captial cases. We, and by we I mean the state/federal government, have to be that sure of someone's guilt. Everytime a criminal sentance is imposed on a defendant, it is done either in the name of the state or in the name of the US government--a body politic that represents YOU, ME, ALL CITIZENS. As such, it is our duty as citizens to participate in the election of judges, serve on juries, and be vocal about law. Without those things, one can only speculate...