These laws make hard cases easy cases. The only reason it didn't work here is because there were some very exceptional circumstances. Even the suspect wasn't sure he had not done it and the combination of DNA evidence + plea bargaining skews terribly against suspects, even innocent ones.

DNA evidence is like a magic bullet for crime, DNA found -> guilty is the norm, not the exception.

As far as the statistics are concerned: we do not actually know the false positive rate.