Somewhat disappointing, but not surprising that they did not describe their actual calculation technique for finding the connected primes. It strikes me that there isn't a good excuse for having bad random numbers with the computation power we now have. A simple bitwise addition of various sources of supposedly random numbers is strictly stronger than any subset of its components. So we can combine lots of questionable strong sources and get a very strong source.
Generating the primes locally with insufficient independence seems more understandable than that the same primes are used by independent parties. That hints at a more severe problem with random number generation. Regardless, assuming this is confirmed, it is a significant problem that needs to be hunted down.