That's still very good odds for the DNA match being correct. Probably about the same odds as reaching into a 25 lb bag of shelled navy beans while blindfolded, and on the first try picking up the only one of a different color than the other 4,165.
But even at that, if the life of a man on trial, or his freedom for life, is at stake, I would want to be absolutely certain of the DNA evidence beyond any reasonable doubt before voting guilty. Of course any supporting evidence would be a great help, but in this particular case there isn't a mention of anything else, or did I miss something by reading so fast?
I disagree with the shelled navy bean analogy, since there are enormous existing DNA databases and computer searches for “matching” DNA.
So you’re not reaching into a bag to get a bean, the “right” bean hops out of the bag. And if you “know” that it is the bean you are looking for, because it is the *only* bean like that...