>The statistically likelihood of matches between distinct parties is in some cases well under the population of the world.

In addition to that, there are problems with bias and statistical independence. A given marker is unlikely to be present in exactly 50% of the population, and to the extent that it isn't it can reduce the probability by that amount that a test match is a true match. Meanwhile the suspect pool for a given crime is likely to encompass several (perhaps many) members of the same extended family, who for the obvious reason are significantly more likely than random members of the world population to have the tested markers match one another. Even within a city you will generally see concentrations of specific ethnicities who may have a higher statistical incidence of specific genetic markers than other populations, which can screw up the numbers by an amount that historically hasn't even knowable because we don't have good numbers on the statistical incidence of specific markers within geographical populations.

The place where this is most pernicious is when they get a sample from a crime scene and run it against some "DNA database" to find a hit. Then everybody is talking about the probability that X suspect would match the DNA at the crime scene rather than the probability that someone in the database would match even if the actual perpetrator wasn't in the database.