The birthday problem is different because there are 365 possibilities and every individual can only have 1 out of 365 states. For DNA there are over 300 million variants in the human genome and you can have different combinations of these variants. As far as matching 9 of 13 loci, thats not surprising to me nor concerning. If you left a sample at a crime scene it would match all 13 loci. Today the FBI uses at least 20 loci.

On top of that, merely being a dna match does not mean you are going to jail. You need corroborating evidence just like how finger prints are used. The odds of a false positive that 1) is a dna match and 2) was in the right place at the right time and lacks and alibi and has a potential motive for the crime must be a trillion to one.