The notion of "reasonable doubt" means that there must be some plausible theory, other than the defendant's guilt, which fits the evidence. In some cases, the existence of such theories will be obvious to the jury even without the defense's help. In most cases, though, the defense will help the jury to come up with some.
It should be noted that a key aspect of plausibility has to do with the defense's conduct in a courtroom. Suppose someone was observed committing a crime in front of many eyewitnesses, and was also clearly photographed in the act. If such a person were to hypothesize in court that the actions were in fact performed by his twin brother, but failed to provide any evidence of the existence of such a twin, would you accept such explanation? Suppose instead, however, that the person presented in court birth records that showed that a twin existed, and further subpoenaed and presented in court further evidence showing that the twin existed and very strongly resembled then defendant. What would you think then?
In a case such as that, I would expect a reasonable jury member to suspect that if a person had a twin brother the person would be able to produce evidence to that effect. A failure to introduce any such evidence would suggest that the theory, which might be plausible (given the right evidence), was likely a fantasy.
You seem willing to execute someone for a murder they didn't commit when all they're guilty of is a simple lapse of judgement (and a potentially FAR less serious crime).
To believe that there is any plausible likelihood that Scott Peterson is innocent, you must believe either:
I don't have to believe anything, if the state's case does not convince me. It does not.
I believe he probably did it. I do not believe the state met its burden. For him to be convicted despite that diminishes everyone's rights to a fair trial.