Your logic is solid, but I think you can reasonably put your objection to bed as it is not pratcial, it is not rational, given the facts.What I am saying (sorry for the OT)is it makes no sense to worry about something that is demonstrably not happening.
In the last 50 years not a single verfied execution has occured in US, that was not valid. I think everyone can accept that if they had any proof of such malfeasance, they would trumpet it all over the world.
The anti captial punishment crowd has been scouring the record for such a case and still has not documented one. Yes many have been set free after being on death row for years, some were even not guilty.
So if the charge was just that inocents are convited, you would be correct.