As best I can make out, the PR is claiming that someone can "make a near perfect prediction" of something that it simultaneously claims results from synapses that "randomly bump into each other". Hm, okay.

It's like describing as "a near perfect prediction", the prediction that a tossed coin will come down heads with 50% probability. The 50% figure may be really precise, but that still tells you nothing about the next coin toss. The press release seems to confuse knowledge about a distribution with knowledge about individuals drawn from it.

As I understand it, what the paper, and Henry Markram as quoted in the press release, are actually saying is that their experiments show a distribution of connections that one would get by things randomly bumping into each other. This implies the predictions that there is no other organising mechanism in play yet to be discovered, and that to build an artificial network capable of the same functionality, one can build the connections in the same random manner. Or as they put it in the title, "Statistical connectivity provides a sufficient foundation for specific functional connectivity".

Note that the title is a prediction from what they have observed, not the observation itself. Functional comparisions of real neural tissue and artificial networks constructed on these lines have not yet been done.