[MisterBastahrd]

No.

The point of the thought experiment is that innocent people are being murdered by the state from time to time for crimes they did not personally commit.

The purpose is essentially "if you are willing to put enough trust in the state to get it right every single time in capital cases, then shouldn't it follow that you be willing to put your own life on the line in the even that the state turns out to be wrong?"

They don't believe it would ever happen to them. Support for the death penalty is support for the state to have the power to end your own life, too.