My bet is that they are not seeing true variations in the decay rate at all. I'd bet on an instrumentation problem, where the decay measurement has a slight temperature or humidity dependence, giving rise to a false annual signal.
That is certainly something that needs to be addressed before any claims are made. The recent fasther-than-light neutrino observation falls under this as well. If this is a real observation then it should be turned over to the scientific community for further scrunity, especially the error introduced by the instrumentation itself.