Challenging DNA evidence with Odds Ratios

I guess the 4yo was lucky the lab identified another suspect... intuitively this sort of error should plague all "dragnet" type DNA "investigations". How would an innocent person defend himself 33 years after a crime was committed? No alibi could survive such a long time. I would have no problems with DNA as one of several pieces of evidence, but by itself I'm going to hang any jury I sit on. This is a good reason to keep one's DNA out of the databases if at all possible.

I'm confused. If you've used DNA evidence to find a person, how can you then use the DNA evidence (as if it were an independent factor) to convict?

Isn't there another component to the probability story here?

We're not just interested in the probability that Leiterman was at the crime scene vs. that the sample was cross-contaminated. We're interested in the probability that Leiterman was at the crime scene AND by sheer happenstance, his DNA happened to be processed by the same crime lab at the same time as the sample from the case vs. the probability that the sample was cross-contaminated.

I don't know the background on how Leiterman's DNA happened to come to the lab in the first place (edit: apparently, a completely separate prescription drug offense), but it strikes me as highly unlikely that a person would be at a crime scene and then by sheer happenstance have their DNA processed by the same crime lab at the same time as the victim's years later.

This may be useful to those of you interested in "solving" this problem: https://betterexplained.com/articles/an-intuitive-and-short-...

First thing is that odds ratios are flawed evidence, because they are independent. You cannot easily combine them or take other evidence into account. Likelihood ratios with well chosen prior probabilities please.