Classic case of letting perfect be the enemy of good. Try harder next time, jj999.
DNA would be significantly harder to fake over 35 years when you're still walking around with your own DNA. Is it perfect? No, but it's a lot more trustworthy in this case than an SSN or driver's license were.
The danger is that a contaminated sample is recorded under your name and the other person commits a crime. Your freedom is contingent on the diligence of an underpaid lab tech.
But you don't need DNA to prove it though. You have interacted with other people in the past. Parents, siblings, relatives, school mates, teachers, bosses, medical records, taxes etc.
If imperfect is fine then all of these are options too.
I did read the article, which clearly stated that after they had sent an innocent man into a mental institution against his will a detective decided to track down the man's father. And a DNA test proved that what the innocent man said was true.
Which begs the question: why was the judge/court so incompetent/malicious that they didn't do that in the first place?