Avi, I am not talking about 2 witnesses, I am talking about circumstantial evidence. And the Rambam says that we are not allowed to use that because, as he explicitly says, we will accept lower and lower percentages and we will eventually kill an innocent man. So this isthe whole point of the Rambam, how he understands the Mitzvah of ???? ????? ?? ?????. The Rambam makes the argument of a slippery slope as to why we can’t use circumstantial evidence that is 100% because we will then come to use 80% and 80% cannot be used because that will inevitably kill an innocent man. So he says that the problem with 100% is that it will lead to 80%. And the problem is that since 80% is certainly not acceptable, we may not even use 100% because it may lead to 80%. And 80% means killing an innocent man one day.
So 1. according to the Rambam even 100% circumstantial evidence may not be used even in the case of a king (and surely not 80%) but we need proof (Dovid in that case with the ger amaleiki was relying on proof from his statement), and 2. The bigger point as it relates to capital punishment in America, there is absolutely no suggestion anywhere in the Torah, or in morals, that a person can be put to death if we have any doubt as to his guilt. And the Rambam does not say this at all. See the Ohr Sameach on the Rambam in Melachim who does not understand how the king can rely on 1 witness in a matter of life and death, even though this is not a bais din. He says that this is learned from the fact that a ben noach can be put to death based on 1 witness. So even though this is not a bais din it is clear that we can only put a person to death if we are certain of his guilt.